Question 1

Which of the following best describes the domain of the function $$f(x) = \log_b(x)$$ where $$b \u003e 0$$ and $$b 
eq 1$$?

Accepted Answer

$$(0, \infty)$$

Question 2

Rewrite $$2 = \log_5$(x) in $$exponential form.

Accepted Answer

$$x = 5^2$

Question 3

Evaluate $$\log_3$(9).$$

Accepted Answer

$$2$$

Question 4

Which of the following statements is TRUE about the graph of $$g(x) = \log_b(x)$$ for $$0 \u003c b \u003c 1$$?

Accepted Answer

The function is decreasing for all $$x \u003e 0.$$

Question 5

What is the value of $$\log_{25}(5)$$?

Accepted Answer

$$\frac{1}{2}$$

Question 6

If $$f(x) = \log_4$(x-5)$$, what is the domain of $$f$$?

Accepted Answer

$$(5, \infty)$$

Question 7

Which property of logarithms justifies that $$\log_b(b^x) = x$$?

Accepted Answer

Inverse property

Question 8

Evaluate $$\log_{10}(100).$$

Accepted Answer

$$2$$

Question 9

Which transformation will shift the graph of $$f(x) = \log_b(x)$$ three units to the right?

Accepted Answer

$$g(x) = \log_b(x-3)$$

Question 10

If $$f(x) = \ln(4-x)$$, what is the domain of $$f$$?

Accepted Answer

$$(-\infty, 4)$$

Question 11

Which of the following is equivalent to $$y = \ln(33)$$?

Accepted Answer

$$e^y = 33$$

Question 12

What is the range of the logarithmic function $$f(x) = \log_b(x)$$ for $$b \u003e 0$$, $$b 
eq 1$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 13

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

Accepted Answer

$$\log_b(0) = 1$$

Question 14

If $$f(x) = \ln(x^2$)$$, what is the domain of $$f$$?

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Question 15

Which transformation reflects the graph of $$f(x) = \log_b(x)$$ about the y-axis?

Accepted Answer

$$g(x) = \log_b(-x)$$

Question 16

A scientist is modeling the pH of a solution using $$	ext{pH} = -\log_{10}([H^+]). If$$ $$[H^+] = 10$$^{-7}$$, what is the pH?

Accepted Answer

$$7$$

Question 17

Which of the following is the correct inverse relationship for $$f(x) = b^x$$?

Accepted Answer

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

Question 18

Which of the following expressions is undefined?

Accepted Answer

$$\log_3$(-3)$$

Question 19

If $$g(x) = \log_2$(4x)$$, what transformation has been applied to $$f(x) = \log_2$(x)$$?

Accepted Answer

Horizontal shrink by a factor of 4

Question 20

Which of the following statements about the graph of $$f(x) = \log_b(x) is $$correct?

Accepted Answer

It passes through the point $$(1,0)$$

Logarithmic Functions: Definitions, Properties, and Graphs

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