Question 1

Which of the following statements correctly describes the relationship between exponential and logarithmic functions?

Accepted Answer

The logarithmic function is the inverse of the exponential function.

Question 2

Given $$f(x) = \log_2$ x$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x \u003e 0$$

Question 3

Rewrite the equation $$2^x = 7 in $$logarithmic form.

Accepted Answer

$$x = \log_2$ 7$$

Question 4

Evaluate $$\log_4$ 64.$$

Accepted Answer

$$3$$

Question 5

If $$\log_b x = y$$, which of the following is the equivalent exponential form?

Accepted Answer

$$b^y = x$$

Question 6

What is the value of $$\log_2$ 1$$?

Accepted Answer

$$0$$

Question 7

Which property of logarithms allows you to write $$\log_b (xy) = \log_b x + \log_b y$$?

Accepted Answer

Product property

Question 8

Find the domain of $$f(x) = \ln(x-5).$$

Accepted Answer

$$x \u003e 5$$

Question 9

Evaluate $$\log_3$ 81.$$

Accepted Answer

$$4$$

Question 10

Which of the following is the graph of $$f(x) = \log_2$ x$$ reflected over the line $$y = x$$?

Accepted Answer

$$f(x) = 2^x$$

Question 11

If $$\log_b a = c$$, what is $$a in $$terms of $$b$$ and $$c$$?

Accepted Answer

$$a = b^c$$

Question 12

Which of the following is NOT a property of logarithms?

Accepted Answer

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

Question 13

Evaluate $$\ln e^2$.

Accepted Answer

$$2$$

Question 14

Given $$f(x) = \log_5$ (x-2)$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x \u003e 2$$

Question 15

If $$\log_2$ x = 4$$, what is the value of $$x$$?

Accepted Answer

$$16$$

Question 16

Which of the following is the correct logarithmic form of $$10^x = 100$$?

Accepted Answer

$$x = \log_{10} 100$$

Question 17

Evaluate $$\log_8$ 2.$$

Accepted Answer

$$\frac{1}{3}$$

Question 18

If $$f(x) = \log_2$ (x^2$ - 9)$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x  3$$

Question 19

Which of the following is true about the graph of $$f(x) = \log_b x$$ for $$b \u003e 1$$?

Accepted Answer

It passes through the point $$(1, 0)$$ and increases slowly for large $$x.$$

Question 20

A scientist measures the pH of a solution as $$pH = -\log_{10} [H^+]. If$$ $$[H^+] = 10$$^{-7}$$, what is the pH?

Accepted Answer

$$7$$

Logarithmic Functions: Definitions, Properties, and Applications

Study Guide - Practice Questions