6. Exponential & Logarithmic Functions

Introduction to Logarithms

6. Exponential & Logarithmic Functions

Introduction to Logarithms

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Logarithms Introduction

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Properties of Logarithms - Everything You Need to Know!

20:37

Properties of Logarithms - Everything You Need to Know!

Writing a Logarithm in Exponential Form

Properties of Logarithms - Everything You Need to Know!

Writing a Logarithm in Exponential Form

Properties of Logarithms - Part 1

Log of 1 and Log Base b of b<sup>n</sup>

Properties of Logarithms - Everything You Need to Know!

Properties of Logarithms - Part 1

Properties of Logarithms - Part 2 - Solving Logarithmic Equations

A Proof of the Logarithm Properties

Change of Base Formula for Logarithms

Logarithms : Expanding and Combining , Example 1

Logarithms : Expanding and Combining , Example 2

Logarithms : Expanding and Combining , Example 3

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Multiple Choice

Change the following logarithmic expression to its equivalent exponential form.

$\log_4x=5$

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Multiple Choice

Change the following logarithmic expression to its equivalent exponential form.

$x=\log9$

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Multiple Choice

Change the following exponential expression to its equivalent logarithmic form.

$3^{x}=7$

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Multiple Choice

Change the following exponential expression to its equivalent logarithmic form.

$e^9=x+3$

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Multiple Choice

Evaluate the given logarithm.

$\log_77^{0.3}$

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Multiple Choice

Evaluate the given logarithm.

$\frac32\log1$

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Multiple Choice

Evaluate the given logarithm.

$\log_9\frac{1}{81}$

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Textbook Question

In Exercises 1–8, write each equation in its equivalent exponential form. 4 = log₂ 16

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Textbook Question

In Exercises 1–8, write each equation in its equivalent exponential form. 2 = log3 x

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Textbook Question

In Exercises 1–8, write each equation in its equivalent exponential form. 2 = log9 x

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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 1–8, write each equation in its equivalent exponential form. log6 216 = y

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Textbook Question

In Exercises 9–20, write each equation in its equivalent logarithmic form. 5^4 = 625

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Textbook Question

In Exercises 9–20, write each equation in its equivalent logarithmic form. 2^-4 = 1/16

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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. 3^4 = 81

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Textbook Question

In Exercises 13–15, write each equation in its equivalent exponential form. 1/2 = log49 7

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Textbook Question

In Exercises 9–20, write each equation in its equivalent logarithmic form. ∛8 = 2

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Textbook Question

In Exercises 9–20, write each equation in its equivalent logarithmic form. 13^2 = x

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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

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￬5 5 = 1

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Textbook Question

In Exercises 9–20, write each equation in its equivalent logarithmic form. b^3 = 1000

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Textbook Question

In Exercises 16–18, write each equation in its equivalent logarithmic form. 13^y = 874

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Textbook Question

In Exercises 9–20, write each equation in its equivalent logarithmic form. 7^y = 200

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Textbook Question

In Exercises 19–29, evaluate each expression without using a calculator. If evaluation is not possible, state the reason. log5 (1/5)

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Textbook Question

Solve each equation. x = log￬3 1/81

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Textbook Question

In Exercises 21–42, evaluate each expression without using a calculator. log4 16

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Textbook Question

In Exercises 21–42, evaluate each expression without using a calculator. log4 16

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Textbook Question

In Exercises 19–29, evaluate each expression without using a calculator. If evaluation is not possible, state the reason. log16 4

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Textbook Question

Solve each equation. log￬x 27/64 = 3

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Textbook Question

In Exercises 21–42, evaluate each expression without using a calculator. log2 64

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Textbook Question

Solve each equation. x = log￬8 ∜8

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Textbook Question

In Exercises 21–42, evaluate each expression without using a calculator. log2 64

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Textbook Question

Solve each equation. x = log￬7 ⁵√7

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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

In Exercises 21–42, evaluate each expression without using a calculator. log5 (1/5)

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Textbook Question

In Exercises 19–29, evaluate each expression without using a calculator. If evaluation is not possible, state the reason. ln e^5

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Textbook Question

In Exercises 21–42, evaluate each expression without using a calculator. log2 (1/8)

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Textbook Question

In Exercises 21–42, evaluate each expression without using a calculator. log7 √7

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Textbook Question

Solve each equation. log￬x 25 = -2

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Textbook Question

In Exercises 21–42, evaluate each expression without using a calculator. log2 (1/√2)

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Textbook Question

Solve each equation. log￬4 x = 3

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Textbook Question

Solve each equation. log￬2 x = 3

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Textbook Question

In Exercises 21–42, evaluate each expression without using a calculator. log64 8

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Textbook Question

Solve each equation. x = log￬4 ∛16

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Textbook Question

In Exercises 32–35, the graph of a logarithmic function is given. Select the function for each graph from the following options: f(x) = logx, g(x) = log(-x), h(x) = log(2-x), r(x)= 1+log(2-x)

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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

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 21–42, evaluate each expression without using a calculator. log4 1

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Textbook Question

Solve each equation. log￬1/3 (x+6) = -2

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Textbook Question

In Exercises 39–40, graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain and range. f(x) = log x and g(x) = - log (x+3)

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Textbook Question

In Exercises 21–42, evaluate each expression without using a calculator. log5 5^7

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Textbook Question

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Textbook Question

In Exercises 21–42, evaluate each expression without using a calculator. 8^(log8 19)

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Textbook Question

Solve each equation. 3x - 15 = log￬x 1 (x>0, x≠1)

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Textbook Question

In Exercises 43– 48, match the function with its graph from choices A–F. ƒ(x) = log￬2 x

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Textbook Question

Graph f(x) = (1/2)^x and g(x) = log(1/2) x in the same rectangular coordinate system.

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Textbook Question

Graph each function. ƒ(x) = log￬10 x

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Textbook Question

Graph each function. ƒ(x) = log￬6 (x-2)

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Textbook Question

In Exercises 53-58, begin by graphing f(x) = log₂ x. Then use transformations of this graph to graph the given function. What is the vertical asymptote? Use the graphs to determine each function's domain and range. g(x) = log₂ (x + 1)

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Textbook Question

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Textbook Question

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Textbook Question

The figure shows the graph of f(x) = log x. In Exercises 59–64, 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. g(x) = log(x − 1)

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Textbook Question

Graph each function. Give the domain and range. ƒ(x) = (log￬2 x) + 3

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Textbook Question

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Textbook Question

Graph each function. Give the domain and range. ƒ(x) = | log￬2 (x+3) |

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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

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

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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. g(x) = ln (x+2)

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Textbook Question

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Textbook Question

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Textbook Question

In Exercises 75–80, find the domain of each logarithmic function. f(x) = log5 (x+4)

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Textbook Question

In Exercises 75–80, find the domain of each logarithmic function. f(x) = log (2 - x)

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Textbook Question

In Exercises 75–80, find the domain of each logarithmic function. f(x) = ln (x-2)²

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Textbook Question

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

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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

In Exercises 81–100, evaluate or simplify each expression without using a calculator. 10^(log 33)

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Textbook Question

In Exercises 81–100, evaluate or simplify each expression without using a calculator. In 1

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Textbook Question

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

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Textbook Question

In Exercises 81–100, evaluate or simplify each expression without using a calculator. In e^6

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Textbook Question

In Exercises 81–100, evaluate or simplify each expression without using a calculator. In (1/e^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 81–100, evaluate or simplify each expression without using a calculator. In e^9x

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Textbook Question

In Exercises 81–100, evaluate or simplify each expression without using a calculator. e^(ln 5x^2)

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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 9/4

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Textbook Question

In Exercises 81–100, evaluate or simplify each expression without using a calculator. 10^(log √x)

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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 √30

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Textbook Question

In Exercises 81–100, evaluate or simplify each expression without using a calculator. 10^(log ∛x)

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Textbook Question

In Exercises 101–104, write each equation in its equivalent exponential form. Then solve for x. log3 (x-1) = 2

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Textbook Question

Use properties of logarithms to rewrite each function, then graph. ƒ(x) = log￬3 x+1/9

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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 105–108, evaluate each expression without using a calculator. log5 (log7 7)

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Textbook Question

In Exercises 105–108, evaluate each expression without using a calculator. log5 (log2 32)

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Textbook Question

In Exercises 105–108, evaluate each expression without using a calculator. log2 (log3 81)

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Textbook Question

In Exercises 105–108, evaluate each expression without using a calculator. log (ln e)

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Textbook Question

In Exercises 109–112, find the domain of each logarithmic function. f(x) = ln (x² - x − 2)

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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

Without using a calculator, find the exact value of: [log3 81 - log𝝅 1]/[log2√2 8 - log 0.001]

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Textbook Question

Without using a calculator, find the exact value of log4 [log 3 (log₂ 8)].

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Textbook Question

145. Without using a calculator, determine which is the greater number: log4 60 or log3 40.

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6. Exponential & Logarithmic Functions

Introduction to Logarithms

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