Question 1

Which of the following is the correct equivalent exponential form of $$2 = \log_3$ x$$?

Accepted Answer

$$x = 3^2$

Question 2

What is the value of $$\log_2$ 16$$?

Accepted Answer

$$4$$

Question 3

Which of the following is the domain of the function $$f(x) = \log_2$ (x-5)$$?

Accepted Answer

$$x \u003e 5$$

Question 4

Evaluate $$\log_5$ 1.$$

Accepted Answer

$$0$$

Question 5

Which property allows you to simplify $$\log_b b^x to$$ $$x$$?

Accepted Answer

Inverse property of logarithms

Question 6

If $$\log_2$ x = 5$$, what is the value of $$x$$?

Accepted Answer

$$x = 32$$

Question 7

Which of the following is the correct logarithmic form of $$e^x = 9$$?

Accepted Answer

$$x = \ln 9$$

Question 8

Evaluate $$\log_2$ \sqrt{2}.$$

Accepted Answer

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

Question 9

Find the domain of $$g(x) = \ln(x-3)^2$.

Accepted Answer

$$x 
eq 3$$

Question 10

Which of the following is true about the graph of $$f(x) = \log_{10} x$$?

Accepted Answer

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

Question 11

Evaluate $$\log_{25} 5.$$

Accepted Answer

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

Question 12

Which of the following is the correct equivalent logarithmic form of $$4^x = 25$$?

Accepted Answer

$$x = \log_4$ 25$$

Question 13

Evaluate $$\log_3$ 81.$$

Accepted Answer

$$4$$

Question 14

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

Accepted Answer

$$x = b^y$$

Question 15

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

Accepted Answer

$$7$$

Question 16

Evaluate $$\ln 1.$$

Accepted Answer

$$0$$

Question 17

Which of the following is the domain of $$f(x) = \ln(2-x)$$?

Accepted Answer

$$x \u003c 2$$

Question 18

Simplify $$e^{\ln x}.$$

Accepted Answer

$$x$$

Question 19

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

Accepted Answer

$$2$$

Question 20

Which of the following is the correct equivalent exponential form of $$x = \ln 5$$?

Accepted Answer

$$e^x = 5$$

Exponential and Logarithmic Functions: Properties, Graphs, and Domains

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