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College Algebra : Solving Logarithmic Functions

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Example Questions

Example Question #21 : Solving Logarithmic Functions

Solve for x:

$log_{3}x=3$

Possible Answers:

x=36

x=9

x=27

x=54

Correct answer:

x=27

Explanation:

In order to solve for x in a logarithmic function, we need to change it into exponential form. That looks as follows:

$log_{b}x=y\rightarrow b^{y}=x$

For this problem, manipulate the log and solve:

$log_{3}x=3$

$3^{3}=x$

x=27

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Example Question #22 : Solving Logarithmic Functions

Solve for x:

$log_{2}x=4$

Possible Answers:

x=16

x=2

x=32

x=8

Correct answer:

x=16

Explanation:

In order to solve for x in a logarithmic function, we need to change it into exponential form. That looks as follows:

$log_{b}x=y\rightarrow b^{y}=x$

For this problem, manipulate the log and solve:

$log_{2}x=4$

$2^{4}=x$

x=16

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Example Question #23 : Solving Logarithmic Functions

Solve for x:

$log_{4}x=2$

Possible Answers:

x=2

x=16

x=8

x=64

Correct answer:

x=16

Explanation:

In order to solve for x in a logarithmic function, we need to change it into exponential form. That looks as follows:

$log_{b}x=y\rightarrow b^{y}=x$

For this problem, manipulate the log and solve:

$log_{4}x=2$

$4^{2}=x$

x=16

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Example Question #24 : Solving Logarithmic Functions

Solve for x:

$log_{7}x=3$

Possible Answers:

x=21

x=343

x=2187

x=49

Correct answer:

x=343

Explanation:

In order to solve for x in a logarithmic function, we need to change it into exponential form. That looks as follows:

$log_{b}x=y\rightarrow b^{y}=x$

For this problem, manipulate the log and solve:

$log_{7}x=3$

$7^{3}=x$

x=343

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Example Question #74 : Exponential And Logarithmic Functions

What is the correct value of ? 3log_b (10)=1

Possible Answers:

log(300)

1000

$\frac{1}{1000}$

300

Correct answer:

1000

Explanation:

Divide by three on both sides.

$\frac{3log_b (10)}{3}=\frac{1}{3}$

$log_b (10)=\frac{1}{3}$

If we would recall 10^2 = 100 and $log_{10}(100) = 2$ , this indicates that:

$b^{\frac{1}{3}} = 10$

Cube both sides to isolate b.

$(b^{\frac{1}{3}}) ^3= 10^3$

The answer is: 1000

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Example Question #25 : Solving Logarithmic Functions

What is the value of 3log_4(64) ?

Possible Answers:

Correct answer:

Explanation:

The expression can be rewritten as:

$3log_4(64) = 3(\frac{log(64)}{log (4)}) = 3(\frac{log(4^3)}{log(4^1)}) =3(\frac{3log(4)}{log(4)})$

The answer is:

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Example Question #26 : Solving Logarithmic Functions

Solve this logarithm: $\log_{10} (5x-1)=\log_{10} (x+9)$

Possible Answers:

$x=\frac{5}{2}$

None of these

$x=\frac{1}{5}$

$x=\frac{10}{2}$

$x=\frac{2}{5}$

Correct answer:

$x=\frac{5}{2}$

Explanation:

By the one-to-one property of logarithms we are able to set 5x-1=x+9 and solve.

$5x-1=x+9\rightarrow 5x=x+10\rightarrow 4x=10\rightarrow \boldsymbol{x=\frac{5}{2}}$

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Example Question #76 : Exponential And Logarithmic Functions

Solve the logarithm: $-8-3\ln x=13$

Possible Answers:

$x\approx 1.92 \times 10^{-4}$

$x\approx 9.12 \times 10^{-4}$

$x\approx 3.12 \times 10^{-4}$

$x\approx 3.12 \times 10^{4}$

$x\approx 2.19\times 10^{-4}$

Correct answer:

$x\approx 9.12 \times 10^{-4}$

Explanation:

$-8-3\ln x=13$

add 8 to both sides:

$-3\ln x=21$

divide both sides by -3:

$\ln x=-7$

exponentiate both sides:

$e^{\ln x}=e^{-7}$

$x=\boldsymbol{e^{-7}\approx9.12\times 10^{-4}}$

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College Algebra : Solving Logarithmic Functions

Study concepts, example questions & explanations for College Algebra

All College Algebra Resources

Example Questions

Example Question #21 : Solving Logarithmic Functions

Example Question #22 : Solving Logarithmic Functions

Example Question #23 : Solving Logarithmic Functions

Example Question #24 : Solving Logarithmic Functions

Example Question #74 : Exponential And Logarithmic Functions

Example Question #25 : Solving Logarithmic Functions

Example Question #26 : Solving Logarithmic Functions

Example Question #76 : Exponential And Logarithmic Functions

All College Algebra Resources

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