Question 1

Which of the following is the correct inverse of the function $$f(x) = 3x + 7$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 7}{3}$$

Question 2

Given the function $$f(x) = \frac{2x - 5}{x + 3}$$, which of the following is its inverse?

Accepted Answer

$$f^{-1}(x$$) = \frac{5 + 3x}{2 - x}$$

Question 3

Evaluate $$\log_{5} 125.$$

Accepted Answer

$$3$$

Question 4

Evaluate $$e^{\ln 7}.$$

Accepted Answer

$$7$$

Question 5

Convert the logarithmic equation $$\log_{2} x = 5 to $$its equivalent exponential form.

Accepted Answer

$$x = 2$$^{5}$$

Question 6

Convert the exponential equation $$3^{x} = 81$ to its equivalent logarithmic form.

Accepted Answer

$$x = \log_{3} 81$$

Question 7

Simplify the expression $$\log_{4} 8 + \log_{4} 2$$ using logarithmic properties.

Accepted Answer

$$2$$

Question 8

Simplify $$\ln(e$$^{5}$$) - \ln(e$$^{2}$$).$$

Accepted Answer

$$3$$

Question 9

Solve for $$x$$: $$2^{x} = 20$. Round your answer to four decimal places.

Accepted Answer

$$x = 4.3219$$

Question 10

Solve for $$x$$: $$\log_{3}(x - 2) = 4.$$

Accepted Answer

Question 11

A population of bacteria doubles every 3 hours. If the initial population is 500, what will the population be after 12 hours?

Accepted Answer

$$8000$$

Question 12

The pH of a solution is defined as $$pH = -\log_{10}[H^+]. If$$ $$[H^+] = 1 	imes 10$$^{-5}$$, what is the pH?

Accepted Answer

$$5$$

Question 13

A radioactive substance decays according to $$N(t) = N_0$ e$$^{-0.2t}$$. If N_0$ = 100$$, how much remains after 10 hours? Round to four decimal places.

Accepted Answer

$$13.5335$$

Question 14

Which of the following graphs represents the equation $$y = \log_{2} x$$?

Accepted Answer

A curve passing through $$(1, 0)$$ and increasing slowly for $$x \u003e 1$$

Question 15

Which equation matches a graph that passes through $$(0, 1)$$ and increases rapidly for positive $$x$$?

Accepted Answer

$$y = e$$^{x}$$

Question 16

If $$f(x) = 2$$^{x}$$ and g(x$$) = \log_{2} x$$, which statement is true?

Accepted Answer

$$g(f(x)) = x$$

Question 17

Simplify $$\log_{5} 25 + \log_{5} 5.$$

Accepted Answer

$$3$$

Question 18

Solve for $$x$$: $$\ln(x) = 2.$$

Accepted Answer

$$x = e$$^{2}$$

Question 19

A car depreciates in value according to $$V(t) = 20000 e$$^{-0.15t}$$, where t$ is in years. What is the value after 5 years? Round to four decimal places.

Accepted Answer

$$9417.4767$$

Question 20

Which of the following is the inverse function of $$f(x) = \ln(x - 4)$$?

Accepted Answer

$$f^{-1}(x$$) = $$e^{x} + 4$

Precalculus Chapter 5 Review: Inverses, Logarithms, Exponentials, and Applications

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