Properties of Logarithms

Multiple Choice

Write the log expression as a single log.

$\log_2\frac{1}{9x}+2\log_23x$

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Multiple Choice

Write the log expression as a single log.

$\ln\frac{3x}{y}+2\ln2y-\ln4x$

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Multiple Choice

Write the single logarithm as a sum or difference of logs.

$\log_3\left(\frac{\sqrt{x}}{9y^2}\right)$

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Multiple Choice

Write the single logarithm as a sum or difference of logs.

$\log_5\left(\frac{5\left(2x+3\right)^2}{x^3}\right)$

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Multiple Choice

Evaluate the given logarithm using the change of base formula and a calculator. Use the common log.

$\log_317$

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Multiple Choice

Evaluate the given logarithm using the change of base formula and a calculator. Use the common log.

$\log_967$

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Multiple Choice

Evaluate the given logarithm using the change of base formula and a calculator. Use the natural log.

$\log_841$

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Multiple Choice

Evaluate the given logarithm using the change of base formula and a calculator. Use the natural log.

$\log_23789$

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log5 (7 × 3)

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log7 (7x)

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Textbook Question

In Exercises 1–8, write each equation in its equivalent exponential form. 5= logb 32

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log(1000x)

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log(1000x)

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Textbook Question

Answer each of the following. Write log_3 12 in terms of natural logarithms using the change-of-base theorem.

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log7 (7/x)

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Textbook Question

Answer each of the following. Between what two consecutive integers must log_2 12 lie?

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log(x/100)

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 1. log 10^12

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log4 (64/y)

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log4 (64/y)

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. ln(e^2/5)

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 1. log 0.1

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Textbook Question

In Exercises 13–15, write each equation in its equivalent exponential form. log3 81 = y

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. logb x^3

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 1. . log 63

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Textbook Question

If the statement is in exponential form, write it in an equivalent logarithmic form. If the statement is in logarithmic form, write it in exponential form. log￬√3 81 = 8

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 1. log 0.0022

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log N^(-6)

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log N^(-6)

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. ln 5√x (fifth root of)

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 1. log(387 * 23)

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. logb (x^2 y)

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 1. log 518/342

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 1. log 387 + log 23

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log4 (√x/64)

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log4 (√x/64)

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Textbook Question

In Exercises 21–42, evaluate each expression without using a calculator. log3 27

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Textbook Question

Solve each equation. x = 3^log3 8

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log6 (36/(√(x+1))

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 1. log 518 - log 342

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. logb ((x^2 y)/z^2)

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Textbook Question

For each substance, find the pH from the given hydronium ion concentration to the nearest tenth. See Example 2(a). grapefruit, 6.3*10^-4

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log √(100x)

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log √(100x)

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Textbook Question

For each substance, find the pH from the given hydronium ion concentration to the nearest tenth. See Example 2(a). limes, 1.6*10^-2

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Textbook Question

Use a calculator to find an approximation to four decimal places for each logarithm. ln 144,000

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log ∛(x/y)

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Textbook Question

For each substance, find the pH from the given hydronium ion concentration to the nearest tenth. See Example 2(a). crackers, 3.9*10^-9

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. logb ((√x y^3)/z^3)

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Textbook Question

Find the [H_3O^+] for each substance with the given pH. Write answers in scientific notation to the nearest tenth. See Example 2(b). soda pop, 2.7

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Textbook Question

Use a calculator to find an approximation to four decimal places for each logarithm. log₂/₃ 5/8

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Textbook Question

In Exercises 21–42, evaluate each expression without using a calculator. log5 5

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Textbook Question

Solve each equation. log￬9 x = 5/2

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Textbook Question

Find the [H_3O^+] for each substance with the given pH. Write answers in scientific notation to the nearest tenth. See Example 2(b). beer, 4.8

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log5 ∛((x^2 y)/24)

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log5 ∛((x^2 y)/24)

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Textbook Question

In Exercises 36–38, begin by graphing f(x) = log2 x Then use transformations of this graph to graph the given function. What is the graph's x-intercept? What is the vertical asymptote? Use the graphs to determine each function's domain and range. g(x) = log2 (x-2)

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. ln[(x^3(√(x^2 + 1))/(x + 1)^4]

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Textbook Question

Suppose that water from a wetland area is sampled and found to have the given hydronium ion concentration. Determine whether the wetland is a rich fen, a poor fen, or a bog. See Example 3. 2.49*10^-5

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log [(10x^2∛(1 - x))/(7(x + 1)^2)]

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Textbook Question

Suppose that water from a wetland area is sampled and found to have the given hydronium ion concentration. Determine whether the wetland is a rich fen, a poor fen, or a bog. See Example 3. 2.49*10^-2

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Textbook Question

Suppose that water from a wetland area is sampled and found to have the given hydronium ion concentration. Determine whether the wetland is a rich fen, a poor fen, or a bog. See Example 3. 2.49*10^-7

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. log 5 + log 2

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. log 5 + log 2

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Textbook Question

Solve each problem. Use a calculator to find an approximation for each logarithm. log 398.4

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. ln x + ln 7

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Textbook Question

Solve each problem. Use a calculator to find an approximation for each logarithm. log 3.984

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. log2 (96) - log2 (3)

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln e^1.6

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln 1/e^2

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. log x + 3 log y

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. log x + 3 log y

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln √e

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Textbook Question

In Exercises 50–53, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log4 (√x/64)

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. (1/2)ln x + ln y

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln 28

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. 2 logb x + 3 logb y

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln 0.00013

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Textbook Question

In Exercises 50–53, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. ln ∛(x/e)

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Textbook Question

In Exercises 50–53, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. ln ∛(x/e)

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Textbook Question

Graph each function. ƒ(x) = log￬3 (x-1) + 2

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Textbook Question

In Exercises 54–57, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. log 3 - 3 log x

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. 5 ln x - 2 ln y

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. 5 ln x - 2 ln y

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln (27 * 943)

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Textbook Question

In Exercises 54–57, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. 1/2 ln x - ln y

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. 3 ln x - (1/3) ln y

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln 98/13

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. 4 ln (x + 6) - 3 ln x

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln 27 + ln 943

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Textbook Question

In Exercises 58–59, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. log4 0.863

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Textbook Question

In Exercises 58–59, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. log4 0.863

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. 3 ln x + 5 ln y - 6 ln z

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. 3 ln x + 5 ln y - 6 ln z

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln 98 - ln 13

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln 84 - ln 17

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. (1/2)(log x + log y)

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Textbook Question

Graph each function. Give the domain and range. ƒ(x) = | log￬1/2 (x-2) |

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. (1/2)(log5 x + log5 y) - 2 log5 (x + 1)

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Textbook Question

The figure shows the graph of f(x) = ln x. In Exercises 65–74, use transformations of this graph to graph each function. Graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range.

h(x) = ln (2x)

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. (1/3) [2 ln(x + 5) - ln x - ln (x^2 - 4)]

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. (1/3) [2 ln(x + 5) - ln x - ln (x^2 - 4)]

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. log x + log(x^2 - 1) - log 7 - log(x + 1)

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Textbook Question

In Exercises 71–78, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. log5 13

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Textbook Question

In Exercises 71–78, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. log14 87.5

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Textbook Question

In Exercises 71–78, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. log14 87.5

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Textbook Question

In Exercises 71–78, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. log0.1 17

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Textbook Question

In Exercises 71–78, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. logπ 63

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Textbook Question

Use the change-of-base theorem to find an approximation to four decimal places for each logarithm. See Example 8. log_2 5

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Textbook Question

In Exercises 79–82, use a graphing utility and the change-of-base property to graph each function. y = log3 x

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Textbook Question

In Exercises 79–82, use a graphing utility and the change-of-base property to graph each function. y = log2 (x + 2)

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Textbook Question

Use the change-of-base theorem to find an approximation to four decimal places for each logarithm. See Example 8. log_8 0.59

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Textbook Question

Expand: log8((4√x)/(64y3))

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Textbook Question

Expand: log8((4√x)/(64y3))

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Textbook Question

In Exercises 81–100, evaluate or simplify each expression without using a calculator. log 10^7

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Textbook Question

Use the change-of-base theorem to find an approximation to four decimal places for each logarithm. See Example 8. . log_1/2 3

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Textbook Question

In Exercises 83–88, let logb 2 = A and logb 3 = C and Write each expression in terms of A and C. logb (3/2)

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Textbook Question

Use the change-of-base theorem to find an approximation to four decimal places for each logarithm. See Example 8. log_π e

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Textbook Question

In Exercises 83–88, let logb 2 = A and logb 3 = C and Write each expression in terms of A and C. logb 8

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Textbook Question

In Exercises 83–88, let logb 2 = A and logb 3 = C and Write each expression in terms of A and C. logb √(2/27)

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Textbook Question

Solve: log₂ (x+9) — log₂ x = 1.

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Textbook Question

Solve: log₂ (x+9) — log₂ x = 1.

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Textbook Question

Use the change-of-base theorem to find an approximation to four decimal places for each logarithm. See Example 8. log_√13 12

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Textbook Question

Use the change-of-base theorem to find an approximation to four decimal places for each logarithm. See Example 8. log_√19 5

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Textbook Question

Let u = ln a and v = ln b. Write each expression in terms of u and v without using the ln function. ln (b^4√a)

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Textbook Question

In Exercises 89–102, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. log4 (2x^3) = 3 log4 (2x)

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Textbook Question

In Exercises 89–102, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. log4 (2x^3) = 3 log4 (2x)

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Textbook Question

In Exercises 89–102, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. ln(8x^3) = 3 ln (2x)

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Textbook Question

Given that log￬10 2 ≈ 0.3010 and log￬10 3 ≈ 0.4771, find each logarithm without using a calculator. log￬10 6

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Textbook Question

In Exercises 81–100, evaluate or simplify each expression without using a calculator. e^ln 125

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Textbook Question

In Exercises 89–102, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. x log 10^x = x^2

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Textbook Question

Let u = ln a and v = ln b. Write each expression in terms of u and v without using the ln function. ln √(a^3/b^5)

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Textbook Question

In Exercises 89–102, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. ln(x + 1) = ln x + ln 1

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Textbook Question

In Exercises 89–102, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. ln(x + 1) = ln x + ln 1

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Textbook Question

Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given g(x) = e^x, find g(ln 1/e)

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Textbook Question

In Exercises 89–102, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. ln(5x) + ln 1 = ln(5x)

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Textbook Question

Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given g(x) = e^x, find g(ln ln 5^2)

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Textbook Question

Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given g(x) = e^x, find g(ln 4)

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Textbook Question

In Exercises 89–102, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. ln x + ln(2x) = ln(3x)

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Textbook Question

Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given ƒ(x) = 3^x, find ƒ(log_3 (2 ln 3))

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Textbook Question

Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given ƒ(x) = 3^x, find ƒ(log_3 (ln 3))

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Textbook Question

Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given ƒ(x) = 3^x, find ƒ(log_3 2)

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Textbook Question

Retaining the Concepts. Expand: log7 (5√x/49y^10) fifth root of x

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Textbook Question

In Exercises 89–102, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. log(x + 3) - log(2x) = [log(x + 3)/log(2x)]

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Textbook Question

In Exercises 89–102, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. log(x + 3) - log(2x) = [log(x + 3)/log(2x)]

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Textbook Question

Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given ƒ(x) = log_2 x, find ƒ(2^(2 log_2 2))

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Textbook Question

In Exercises 89–102, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. [log(x + 2)/log(x - 1)] = log(x + 2) - log(x - 1)

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Textbook Question

Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given ƒ(x) = log_2 x, find ƒ(2^(log_2 2))

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Textbook Question

Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given ƒ(x) = log_2 x, find ƒ(2^7)

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Textbook Question

In Exercises 89–102, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. log6 [(x - 1)/(x^2 + 4)] = log6 (x - 1) - log6 (x^2 + 4)

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Textbook Question

Work each problem. Which of the following is equivalent to 2 ln(3x) for x > 0? A. ln 9 + ln x B. ln 6x C. ln 6 + ln x D. ln 9x^2

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Textbook Question

Work each problem. Which of the following is equivalent to ln(4x) - ln(2x) for x > 0? A. 2 ln x B. ln 2x C. (ln 4x)/(ln 2x) D. ln 2

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Textbook Question

In Exercises 89–102, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. log6 [4(x + 1)] = log6 (4) + log6 (x + 1)

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Textbook Question

In Exercises 89–102, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. log6 [4(x + 1)] = log6 (4) + log6 (x + 1)

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Textbook Question

In Exercises 89–102, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. log3 (7) = 1/[log7 (3)]

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Textbook Question

Use properties of logarithms to rewrite each function, then graph. ƒ(x) = log￬2 [4 (x-3) ]

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Textbook Question

Use properties of logarithms to rewrite each function, then graph. ƒ(x) = log￬3 [9 (x+2) ]

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Textbook Question

In Exercises 101–104, write each equation in its equivalent exponential form. Then solve for x. log4 x=-3

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Textbook Question

In Exercises 109–112, find the domain of each logarithmic function. f(x) = log[(x+1)/(x-5)]

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Textbook Question

In Exercises 125–128, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. log7 49 / log7 7 = log7 49 - log7 7

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Textbook Question

In Exercises 125–128, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. logb (x^3 + y^3) = 3 logb x + 3 logb y

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Textbook Question

In Exercises 125–128, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. logb (x^3 + y^3) = 3 logb x + 3 logb y

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Textbook Question

In Exercises 125–128, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. logb (xy)^5 = (logb x + logb y)^5

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Textbook Question

If log 3 = A and log 7 = B, find log7 (9) in terms of A and B.

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6. Exponential & Logarithmic Functions

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