Question 1

Which of the following is the correct formula for the half-life $$h of a $$substance undergoing continuous exponential decay at rate $$k$$?

Accepted Answer

$$h = \frac{\ln(2)}{k}$$

Question 2

Given $$A(t) = A_0$ e$$^{kt}$$, which of the following statements is true if k$$ \u003c 0$$?

Accepted Answer

The function models continuous exponential decay.

Question 3

Solve for $$x$$: $$5^{2x} = 17$

Accepted Answer

$$x = \frac{\ln(17)}{2\ln(5)}$$

Question 4

Expand the following logarithmic expression: $$\log_2$ \left( \frac{x^3$ y^2$}{z^5$} \right)$$

Accepted Answer

$$3\log_2$(x) + 2\log_2$(y) - 5\log_2$(z)$$

Question 5

Condense the following expression: $$2\log_3$(x) + \frac{1}{2}\log_3$(y) - \log_3$(z)$$

Accepted Answer

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

Question 6

If $$f(x) = 3^x$$, which of the following is the correct inverse function?

Accepted Answer

$$f^{-1}(x$$) = \$$log_3(x$$)$$

Question 7

Which of the following is the correct change of base formula for $$\log_a(x)$$?

Accepted Answer

$$\log_a(x) = \frac{\log_b(x)}{\log_b(a)}$$

Question 8

Solve for $$x$$: $$\log_2$(x-1) = 3$$

Accepted Answer

$$x = 9$$

Question 9

Which of the following is NOT a correct property of logarithms?

Accepted Answer

$$\log_a(x+y) = \log_a(x) + \log_a(y)$$

Question 10

A radioactive material decays continuously at a rate $$k = -0.04. $$What is its half-life?

Accepted Answer

$$h = \frac{\ln(2)}{0.04}$$

Question 11

If $$400 is deposited in a bank at 5% annual interest, compounded continuously, what is the amount after 1 year? (Use A$$ = $$Pe^{rt}$)

Accepted Answer

$$A = 400e$$^{0.05}$$ \approx 421.03$$

Question 12

Which of the following best describes the domain of $$f(x) = \log(x)$$?

Accepted Answer

$$x \u003e 0$$

Question 13

Which transformation shifts the graph of $$f(x) = \log(x)$$ two units to the right?

Accepted Answer

$$f(x) = \log(x-2)$$

Question 14

Solve for $$x$$: $$e^{2x} = 7$

Accepted Answer

$$x = \frac{1}{2}\ln(7)$$

Question 15

Which of the following is the correct expanded form of $$\log_2$(2x^3y$$)$?

Accepted Answer

$$1 + 3\log_2$(x) + \log_2$(y)$$

Question 16

Which of the following is the correct condensed form of $$\log_3$(x) + \log_3$(y) - \log_3$(z)$$?

Accepted Answer

$$\log_3$\left( \frac{xy}{z} \right)$$

Question 17

Which of the following is the correct formula for compound interest compounded $$n$$ times per year?

Accepted Answer

$$A = P \left( 1 + \frac{r}{n} \$$right)^{nt}$$

Question 18

Which of the following is true about the range of $$f(x) = a^x$$ for $$a \u003e 0$$ and $$a 
eq 1$$?

Accepted Answer

The range is $$(0, \infty)$$

Exponential and Logarithmic Functions: Precalculus Study Guide

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