6. Exponential & Logarithmic Functions

Introduction to Logarithms

6. Exponential & Logarithmic Functions

# Introduction to Logarithms - Video Tutorials & Practice Problems

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concept

## Logarithms Introduction

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2

concept

## The Natural Log

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3

Problem

ProblemChange the following logarithmic expression to its equivalent exponential form.

$\log_4x=5$

A

$4^{x}=5$

B

$x^4=5$

C

$4^5=x$

D

$5^4=x$

4

Problem

ProblemChange the following logarithmic expression to its equivalent exponential form.

$x=\log9$

A

$x=9$

B

$9^{x}=10$

C

$1^{x}=9$

D

$10^{x}=9$

5

Problem

ProblemChange the following exponential expression to its equivalent logarithmic form.

$3^{x}=7$

A

$\log_37=x$

B

$\log_73=x$

C

$\log_3x=7$

D

$\log7=3^{x}$

6

Problem

ProblemChange the following exponential expression to its equivalent logarithmic form.

$e^9=x+3$

A

$\log\left(x+3\right)=9$

B

$\ln\left(x+3\right)=9$

C

$\ln9=x+3$

D

$\log_9x=e^3$

7

concept

## Evaluate Logarithms

Video duration:

5mPlay a video:

8

Problem

ProblemEvaluate the given logarithm.

$\log_77^{0.3}$

A

1.79

B

7

C

1

D

0.3

9

Problem

ProblemEvaluate the given logarithm.

$\frac32\log1$

A

$\frac32$

B

0

C

1

D

10

10

Problem

ProblemEvaluate the given logarithm.

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

A

81

B

2

C

– 2

D

9

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PRACTICE PROBLEMS AND ACTIVITIES (93)

- In Exercises 1–8, write each equation in its equivalent exponential form. 4 = log₂ 16
- In Exercises 1–8, write each equation in its equivalent exponential form. 2 = log3 x
- In Exercises 1–8, write each equation in its equivalent exponential form. 2 = log9 x
- In Exercises 1–8, write each equation in its equivalent exponential form. 5= logb 32
- In Exercises 1–8, write each equation in its equivalent exponential form. log6 216 = y
- In Exercises 9–20, write each equation in its equivalent logarithmic form. 5^4 = 625
- In Exercises 9–20, write each equation in its equivalent logarithmic form. 2^-4 = 1/16
- If the statement is in exponential form, write it in an equivalent logarithmic form. If the statement is in lo...
- In Exercises 13–15, write each equation in its equivalent exponential form. 1/2 = log49 7
- In Exercises 9–20, write each equation in its equivalent logarithmic form. ∛8 = 2
- In Exercises 9–20, write each equation in its equivalent logarithmic form. 13^2 = x
- In Exercises 13–15, write each equation in its equivalent exponential form. log3 81 = y
- If the statement is in exponential form, write it in an equivalent logarithmic form. If the statement is in lo...
- In Exercises 9–20, write each equation in its equivalent logarithmic form. b^3 = 1000
- In Exercises 16–18, write each equation in its equivalent logarithmic form. 13^y = 874
- In Exercises 9–20, write each equation in its equivalent logarithmic form. 7^y = 200
- In Exercises 19–29, evaluate each expression without using a calculator. If evaluation is not possible, state ...
- Solve each equation. x = log￬3 1/81
- In Exercises 21–42, evaluate each expression without using a calculator. log4 16
- In Exercises 21–42, evaluate each expression without using a calculator. log4 16
- In Exercises 19–29, evaluate each expression without using a calculator. If evaluation is not possible, state ...
- Solve each equation. log￬x 27/64 = 3
- In Exercises 21–42, evaluate each expression without using a calculator. log2 64
- Solve each equation. x = log￬8 ∜8
- In Exercises 21–42, evaluate each expression without using a calculator. log2 64
- Solve each equation. x = log￬7 ⁵√7
- In Exercises 21–42, evaluate each expression without using a calculator. log3 27
- In Exercises 21–42, evaluate each expression without using a calculator. log5 (1/5)
- In Exercises 19–29, evaluate each expression without using a calculator. If evaluation is not possible, state ...
- In Exercises 21–42, evaluate each expression without using a calculator. log2 (1/8)
- In Exercises 21–42, evaluate each expression without using a calculator. log7 √7
- Solve each equation. log￬x 25 = -2
- In Exercises 21–42, evaluate each expression without using a calculator. log2 (1/√2)
- Solve each equation. log￬4 x = 3
- Solve each equation. log￬2 x = 3
- In Exercises 21–42, evaluate each expression without using a calculator. log64 8
- Solve each equation. x = log￬4 ∛16
- In Exercises 32–35, the graph of a logarithmic function is given. Select the function for each graph from the ...
- In Exercises 21–42, evaluate each expression without using a calculator. log5 5
- In Exercises 36–38, begin by graphing f(x) = log2 x Then use transformations of this graph to graph the given ...
- In Exercises 21–42, evaluate each expression without using a calculator. log4 1
- Solve each equation. log￬1/3 (x+6) = -2
- In Exercises 39–40, graph f and g in the same rectangular coordinate system. Use transformations of the graph ...
- In Exercises 21–42, evaluate each expression without using a calculator. log5 5^7
- In Exercises 39–40, graph f and g in the same rectangular coordinate system. Use transformations of the graph ...
- In Exercises 21–42, evaluate each expression without using a calculator. 8^(log8 19)
- Solve each equation. 3x - 15 = log￬x 1 (x>0, x≠1)
- In Exercises 43– 48, match the function with its graph from choices A–F. ƒ(x) = log￬2 x
- Graph f(x) = (1/2)^x and g(x) = log(1/2) x in the same rectangular coordinate system.
- Graph each function. ƒ(x) = log￬10 x
- Graph each function. ƒ(x) = log￬6 (x-2)
- In Exercises 53-58, begin by graphing f(x) = log₂ x. Then use transformations of this graph to graph the given...
- In Exercises 53-58, begin by graphing f(x) = log₂ x. Then use transformations of this graph to graph the given...
- In Exercises 53-58, begin by graphing f(x) = log₂ x. Then use transformations of this graph to graph the given...
- The figure shows the graph of f(x) = log x. In Exercises 59–64, use transformations of this graph to graph eac...
- Graph each function. Give the domain and range. ƒ(x) = (log￬2 x) + 3
- The figure shows the graph of f(x) = log x. In Exercises 59–64, use transformations of this graph to graph eac...
- Graph each function. Give the domain and range. ƒ(x) = | log￬2 (x+3) |
- Graph each function. Give the domain and range. ƒ(x) = (log￬1/2 x) - 2
- The figure shows the graph of f(x) = log x. In Exercises 59–64, use transformations of this graph to graph eac...
- Graph each function. Give the domain and range. ƒ(x) = log￬1/2 (x-2)
- The figure shows the graph of f(x) = ln x. In Exercises 65–74, use transformations of this graph to graph each...
- The figure shows the graph of f(x) = ln x. In Exercises 65–74, use transformations of this graph to graph each...
- The figure shows the graph of f(x) = ln x. In Exercises 65–74, use transformations of this graph to graph each...
- In Exercises 75–80, find the domain of each logarithmic function. f(x) = log5 (x+4)
- In Exercises 75–80, find the domain of each logarithmic function. f(x) = log (2 - x)
- In Exercises 75–80, find the domain of each logarithmic function. f(x) = ln (x-2)²
- In Exercises 81–100, evaluate or simplify each expression without using a calculator. log 100
- In Exercises 81–100, evaluate or simplify each expression without using a calculator. log 10^7
- In Exercises 81–100, evaluate or simplify each expression without using a calculator. 10^(log 33)
- In Exercises 81–100, evaluate or simplify each expression without using a calculator. In 1
- In Exercises 81–100, evaluate or simplify each expression without using a calculator. In e
- In Exercises 81–100, evaluate or simplify each expression without using a calculator. In e^6
- In Exercises 81–100, evaluate or simplify each expression without using a calculator. In (1/e^6)
- In Exercises 81–100, evaluate or simplify each expression without using a calculator. e^ln 125
- In Exercises 81–100, evaluate or simplify each expression without using a calculator. In e^9x
- In Exercises 81–100, evaluate or simplify each expression without using a calculator. e^(ln 5x^2)
- Given that log￬10 2 ≈ 0.3010 and log￬10 3 ≈ 0.4771, find each logarithm without using a calculator. log￬10 9/4
- In Exercises 81–100, evaluate or simplify each expression without using a calculator. 10^(log √x)
- Given that log￬10 2 ≈ 0.3010 and log￬10 3 ≈ 0.4771, find each logarithm without using a calculator. log￬10 √30
- In Exercises 81–100, evaluate or simplify each expression without using a calculator. 10^(log ∛x)
- In Exercises 101–104, write each equation in its equivalent exponential form. Then solve for x. log3 (x-1) = 2
- Use properties of logarithms to rewrite each function, then graph. ƒ(x) = log￬3 x+1/9
- In Exercises 101–104, write each equation in its equivalent exponential form. Then solve for x. log4 x=-3
- In Exercises 105–108, evaluate each expression without using a calculator. log5 (log7 7)
- In Exercises 105–108, evaluate each expression without using a calculator. log5 (log2 32)
- In Exercises 105–108, evaluate each expression without using a calculator. log2 (log3 81)
- In Exercises 105–108, evaluate each expression without using a calculator. log (ln e)
- In Exercises 109–112, find the domain of each logarithmic function. f(x) = ln (x² - x − 2)
- In Exercises 109–112, find the domain of each logarithmic function. f(x) = log[(x+1)/(x-5)]
- Without using a calculator, find the exact value of: [log3 81 - log𝝅 1]/[log2√2 8 - log 0.001]
- Without using a calculator, find the exact value of log4 [log 3 (log₂ 8)].
- 145. Without using a calculator, determine which is the greater number: log4 60 or log3 40.