Question 1

Which of the following statements is TRUE about the domain and range of the logarithmic function $$y = \log_a x$$ where $$a \u003e 0$$ and $$a 
eq 1$$?

Accepted Answer

The domain is $$(0, \infty)$$ and the range is $$(-\infty, \infty).$$

Question 2

Evaluate $$\log_{10} 2.5$$ using a calculator. Which value is closest?

Accepted Answer

0.398

Question 3

Which property of logarithms justifies that $$\log_a a = 1$$?

Accepted Answer

Because $$a^1 = a$

Question 4

If $$y = \log_a x$$, which of the following points is always on its graph?

Accepted Answer

$$(1, 0)$$

Question 5

Which of the following is the correct solution to $$\log_3$ (4x - 7) = 2$$?

Accepted Answer

$$x = 4$$

Question 6

What is the value of $$\ln(-1)$$?

Accepted Answer

Undefined

Question 7

Which of the following describes the behavior of $$y = \log_a x$$ when $$0 \u003c a \u003c 1$$?

Accepted Answer

The function is decreasing.

Question 8

Solve for $$x$$: $$e^{2x} = 5$.

Accepted Answer

$$x = \frac{1}{2} \ln 5$$

Question 9

Which of the following is NOT a property of logarithms?

Accepted Answer

$$\log_a 0 = 1$$

Question 10

Which of the following is the correct inverse relationship for $$y = \log_a x$$?

Accepted Answer

$$x = a^y$$

Question 11

A scientist is measuring the pH of a solution, which is defined as $$	ext{pH} = -\log_{10} [H^+]. If$$ $$[H^+] = 1 	imes 10$$^{-4}$$, what is the pH?

Accepted Answer

4

Question 12

Which of the following is the vertical asymptote of the function $$y = \log_a x$$?

Accepted Answer

The y-axis ($$x = 0)$$

Question 13

If $$y = \log_2$(x-1) + 3$$, what is the domain of the function?

Accepted Answer

$$(1, \infty)$$

Question 14

Which of the following is equivalent to $$\log_e x$$?

Accepted Answer

$$\ln x$$

Question 15

If $$\log_a x = y$$, which of the following is true?

Accepted Answer

$$x = a^y$$

Question 16

Which of the following is the correct value for $$\log_{10} \left(\frac{1}{3}\right)$$?

Accepted Answer

$$-0.477$$

Question 17

Which of the following is a real-world application of logarithms?

Accepted Answer

Measuring the intensity of earthquakes (Richter scale)

Question 18

If $$y = \log_a x$$ and $$a \u003e 1$$, what is the behavior of the function?

Accepted Answer

It is increasing.

Question 19

Which of the following is the correct solution to $$\ln x = 3$$?

Accepted Answer

$$x = e^3$

Question 20

Which of the following is the correct solution to $$\log_2$ x = -1$$?

Accepted Answer

$$x = \frac{1}{2}$$

Logarithms and Their Properties: Precalculus Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards