Question 1

Which of the following is equivalent to $\log_3 81 = x$ in exponential form?

Accepted Answer

$3^x = 81$

Question 2

Evaluate $\log_5 1$ without using a calculator.

Accepted Answer

$0$

Question 3

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

Accepted Answer

Product Rule

Question 4

Expand the expression $\log_2 \left( \dfrac{8x^3}{y} \right)$ using properties of logarithms.

Accepted Answer

$3\log_2 x + \log_2 8 - \log_2 y$

Question 5

Condense the expression $2\log_3 x - \dfrac{1}{2}\log_3 y$ into a single logarithm.

Accepted Answer

$\log_3 \left( \dfrac{x^2}{\sqrt{y}} \right)$

Question 6

Solve for $x$: $\log_4 x = 3$.

Accepted Answer

$x = 64$

Question 7

Which of the following statements is TRUE?

Accepted Answer

$\log_b b = 1$

Question 8

Rewrite $\log_2 32$ as a product of an integer and $\log_2 2$.

Accepted Answer

$5\log_2 2$

Question 9

If $\log_7 x = 2$, what is the value of $x$?

Accepted Answer

$49$

Question 10

Which of the following is the correct application of the change of base formula for $\log_5 12$?

Accepted Answer

$\dfrac{\log_{10} 12}{\log_{10} 5}$

Question 11

Evaluate $\log_3 1$.

Accepted Answer

$0$

Question 12

Which of the following is equivalent to $\log_b (x^k)$?

Accepted Answer

$k \log_b x$

Question 13

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

Accepted Answer

$7$

Question 14

Solve for $x$: $2^{3x} = 16$.

Accepted Answer

$x = \dfrac{2}{3}$

Question 15

Which of the following is the correct expansion of $\log_5 \left( \dfrac{25x^2}{y^3} \right)$?

Accepted Answer

$2\log_5 x + 2\log_5 5 - 3\log_5 y$

Question 16

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

Accepted Answer

$32$

Question 17

Condense the expression $\log_4 x + \log_4 y - \log_4 z$ into a single logarithm.

Accepted Answer

$\log_4 \left( \dfrac{xy}{z} \right)$

Question 18

Solve for $x$: $\log_3 (x - 2) = 4$.

Accepted Answer

$x = 83$

Question 19

Which of the following is NOT a valid property of logarithms?

Accepted Answer

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

Question 20

A radioactive substance decays according to $A = A_0 e^{-kt}$. If $A_0 = 100$ grams, $A = 25$ grams after $t = 10$ years, what is the value of $k$? (Round to 3 decimal places.)

Accepted Answer

$k = 0.139$

C4

Study Guide - Practice Questions

Study Guide - Flashcards