Question 1

Which of the following best describes the logarithm function?

Accepted Answer

It is the inverse operation of exponentiation.

Question 2

Rewrite the equation $3^4 = 81$ in logarithmic form.

Accepted Answer

$\log_3 81 = 4$

Question 3

Convert $\log_{10} 1000 = x$ to its equivalent exponential form.

Accepted Answer

$10^x = 1000$

Question 4

Which property of logarithms allows you to write $\log_b b = 1$?

Accepted Answer

Identity Property

Question 5

Evaluate $\log_2 8$.

Accepted Answer

3

Question 6

Which of the following is equivalent to $e^{x} = 5$ in logarithmic form?

Accepted Answer

$\ln 5 = x$

Question 7

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

Accepted Answer

$b^y = x$

Question 8

Evaluate $\log_{10} 0.01$.

Accepted Answer

$-2$

Question 9

Which of the following statements is true about the natural logarithm?

Accepted Answer

It is denoted as $\ln x$ and has base $e$.

Question 10

Which property of logarithms is used to evaluate $\log_b 1$?

Accepted Answer

Zero Property

Question 11

A scientist is analyzing 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 12

Rewrite $5^x = 25$ in logarithmic form.

Accepted Answer

$\log_5 25 = x$

Question 13

Evaluate $\log_3 1$.

Accepted Answer

0

Question 14

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

Accepted Answer

$e^2 = x$

Question 15

If $\log_4 x = 3$, what is the value of $x$?

Accepted Answer

64

Question 16

Which of the following is NOT a property of logarithms?

Accepted Answer

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

Question 17

Evaluate $\log_5 25$.

Accepted Answer

2

Question 18

If $\log_2 x = 5$, what is $x$?

Accepted Answer

32

Question 19

Which of the following is the correct logarithmic form of $2^x = 16$?

Accepted Answer

$\log_2 16 = x$

Question 20

Evaluate $\log_{10} 1$.

Accepted Answer

0

Introduction to Logarithms: Definitions, Conversions, and Properties

Study Guide - Practice Questions