$$y = \log_a x$$ \text{ if and only if } x = a^y$

Question 1

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

Accepted Answer

$$y = \log_a x$$ 	ext{ if and only if } x = a^y$

Question 2

What is the domain of the logarithmic function $$f(x) = \log_3$(x + 2)$$?

Accepted Answer

$$x \u003e -2$$

Question 3

Convert the exponential equation $$e^u = 25 to $$its equivalent logarithmic form.

Accepted Answer

$$u = \ln 25$$

Question 4

Evaluate $$\log_3$ 81.$$

Accepted Answer

$$4$$

Question 5

Which of the following describes the range of the logarithmic function $$y = \log_a x$$?

Accepted Answer

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

Question 6

If $$y = \log_4$ x$$, what is the equivalent exponential statement?

Accepted Answer

$$x = 4^y$$

Question 7

Find the exact value of $$\log_5$ \frac{1}{125}.$$

Accepted Answer

$$-3$$

Question 8

Which transformation is applied to the graph of $$y = \ln x to $$obtain $$y = -\ln(x + 1)$$?

Accepted Answer

Reflect about the x-axis and shift left 1 unit

Question 9

What is the vertical asymptote of the function $$f(x) = -\ln(x + 1)$$?

Accepted Answer

$$x = -1$$

Question 10

Find the inverse of $$f(x) = -\ln(x + 1).$$

Accepted Answer

$$f^{-1}(x$$) = $$e^{-x} - 1$

Question 11

What is the domain of the inverse function $$f^{-1}(x$$) = $$e^{-x} - 1$?

Accepted Answer

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

Question 12

Solve the logarithmic equation $$\log_5$(3x - 4) = 3$$ for $$x.$$

Accepted Answer

$$x = 43$$

Question 13

Which property is true for the graph of $$y = \log_a x$$ when $$0 \u003c a \u003c 1$$?

Accepted Answer

The function is decreasing

Question 14

If $$y = \log x$$, what is the equivalent exponential statement?

Accepted Answer

$$x = 10^y$$

Question 15

Solve the exponential equation $$e^{3x} = 7$ for x$.

Accepted Answer

$$x = \frac{1}{3} \ln 7$$

Question 16

Which of the following points is always on the graph of $$y = \log_a x$$?

Accepted Answer

$$(1, 0)$$

Question 17

What is the domain of $$f(x) = 2\log(x - 2)$$?

Accepted Answer

$$x \u003e 2$$

Question 18

Which real-world scenario best illustrates the use of logarithmic functions?

Accepted Answer

Measuring the intensity of earthquakes on the Richter scale

Question 19

If $$y = \ln x$$, what is the equivalent exponential statement?

Accepted Answer

$$x = e^y$$

Question 20

Which of the following is NOT a property of logarithmic functions?

Accepted Answer

The graph has a y-intercept

Study Guide: Logarithmic Functions in Precalculus

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