Question 1

Which of the following functions is an exponential function?

Accepted Answer

$$f(x) = 3^x$$

Question 2

What is the domain of the exponential function $$f(x) = 2^x$$?

Accepted Answer

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

Question 3

Which transformation occurs when you graph $$g(x) = 2$$^{x-3}$$ + 4$$ compared to $$f(x) = 2^x$$?

Accepted Answer

Shift right 3 units and up 4 units

Question 4

The graph of $$f(x) = 3^x$$ passes through which of the following points?

Accepted Answer

$$(0, 1)$$

Question 5

What is the range of the function $$f(x) = e^x$$?

Accepted Answer

$$(0, \infty)$$

Question 6

Which of the following is the logarithmic form of the equation $$2^x = 8$$?

Accepted Answer

$$\log_2$ 8 = x$$

Question 7

Evaluate $$\log_2$ 16.$$

Accepted Answer

$$4$$

Question 8

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

Accepted Answer

Product Rule

Question 9

What is the solution to the equation $$3^x = 81$$?

Accepted Answer

$$x = 4$$

Question 10

If $$\log_5$ x = 2$$, what is the value of $$x$$?

Accepted Answer

$$x = 25$$

Question 11

Which of the following is the correct change of base formula for $$\log_3$ 20$$?

Accepted Answer

$$\frac{\log 20}{\log 3}$$

Question 12

What is the solution to the logarithmic equation $$\log_2$ (x - 1) = 3$$?

Accepted Answer

$$x = 9$$

Question 13

Which of the following statements about the graph of $$f(x) = \log_3$ x is $$true?

Accepted Answer

The graph has a vertical asymptote at $$x = 0$$

Question 14

Which property of logarithms allows you to write $$\log_b (x^n) as$$ $$n \log_b x$$?

Accepted Answer

Power Rule

Question 15

Solve the exponential equation $$2^{x+1} = 16$.

Accepted Answer

$$x = 3$$

Question 16

Which of the following is the correct logarithmic form for the equation $$5^x = 125$$?

Accepted Answer

$$\log_5$ 125 = x$$

Question 17

If $$f(x) = 2^x$$ and $$g(x) = 2$$^{-x}$$, which statement is true about their graphs?

Accepted Answer

The graph of $$g(x) is a $$reflection of $$f(x)$$ across the $$x-$$axis

Question 18

Which of the following is the solution to $$\log_4$ x = 1.5$$?

Accepted Answer

$$x = 8$$

Question 19

What is the value of $$\log_{10} 1000$$?

Accepted Answer

$$3$$

Inverse, Exponential, and Logarithmic Functions: Study Notes

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