Question 1

Solve for $x$: $2 \log_2(x) + 3 = 0$

Accepted Answer

$x = 2^{-1.5} = \dfrac{1}{2\sqrt{2}}$

Question 2

Which of the following is the solution to $\log_2(x) + \log_2(2x+1) = 0$?

Accepted Answer

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

Question 3

Given $\log_7(x-1) = 2\log_7(x-1)$, what is the solution for $x$?

Accepted Answer

No solution

Question 4

Solve for $x$: $2\ln(x+3) = \ln(x+1) + 3\ln2$

Accepted Answer

$x = 5$

Question 5

If $\log_2(2x-9) = 2 - \log_2(x-1)$, what is the value of $x$?

Accepted Answer

$x = 5$

Question 6

Solve for $x$: $\log_2((x-2)(x-3)) = \log_2 9$

Accepted Answer

$x = 5$ or $x = -1$

Question 7

What is the solution to $\log_3\left(\dfrac{x}{3}\right) = 2$?

Accepted Answer

$x = 27$

Question 8

A biologist models bacteria growth with $N = N_0 e^{kt}$. If $N_0 = 100$, $N = 800$ after 6 hours, what is the value of $k$? (Round to 3 decimal places)

Accepted Answer

$k = 0.231$

Question 9

A radioactive substance decays according to $A = A_0 e^{-0.05t}$. How long will it take for the substance to decay to 25% of its original amount?

Accepted Answer

$t = 27.73$

Question 10

If $\log_b(x) = 3$ and $\log_b(y) = 2$, what is $\log_b\left(\dfrac{x^2}{y^3}\right)$?

Accepted Answer

$6 - 6 = 0$

Question 11

Which of the following is equivalent to $\log_5(25x)$?

Accepted Answer

$2 + \log_5(x)$

Question 12

If $\log_2(x) = 4$, what is the value of $x$?

Accepted Answer

$x = 16$

Question 13

Solve for $x$: $\ln(x^2) = 6$

Accepted Answer

$x = \pm e^3$

Question 14

If $\log_{10}(x) = -2$, what is $x$?

Accepted Answer

$x = 0.01$

Question 15

Which of the following is the correct domain for $f(x) = \log_2(x-4)$?

Accepted Answer

$x > 4$

Question 16

A population doubles every 5 years. If the initial population is 1000, what will it be after 15 years?

Accepted Answer

$4000$

Question 17

If $\log_3(x) = 5$, what is $\log_3(\sqrt{x})$?

Accepted Answer

$2.5$

Question 18

Which property allows you to write $\log_b(MN) = \log_b(M) + \log_b(N)$?

Accepted Answer

Product Property of Logarithms

Question 19

If $\log_4(x) = 3$, what is $x$?

Accepted Answer

$x = 64$

Question 20

Solve for $x$: $\log_2(x) + \log_2(x-2) = 3$

Accepted Answer

$x = 4$

Solving Logarithmic Equations in College Algebra

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