Logarithms Test — 10 Questions

Question 1

Compute $\log_2 8$.

Accepted Answer

$3$

Answer

$2$

Answer

$4$

Answer

$8$

Question 2

Compute $\log_3 81$.

Accepted Answer

$4$

Answer

$2$

Answer

$3$

Answer

$9$

Question 3

Compute $\log_5 \dfrac{1}{25}$.

Accepted Answer

$-2$

Answer

$-1$

Answer

$1$

Answer

$2$

Question 4

Using $\log_a(xy) = \log_a x + \log_a y$, compute $\log_2(4 \cdot 8)$.

Accepted Answer

$5$

Answer

$3$

Answer

$6$

Answer

$32$

Question 5

Compute $\log_3 27 - \log_3 3$.

Accepted Answer

$2$

Answer

$1$

Answer

$3$

Answer

$9$

Question 6

Compute $\log_2(2^{10})$.

Accepted Answer

$10$

Answer

$2$

Answer

$5$

Answer

$1024$

Question 7

Solve for $x$: $\log_2 x = 4$.

Accepted Answer

$16$

Answer

$2$

Answer

$8$

Answer

$32$

Question 8

If $\log_a 5 = 2$, what is $a$? (Assume $a > 0$, $a 
eq 1$.)

Accepted Answer

$\sqrt{5}$

Answer

$2$

Answer

$5$

Answer

$25$

Question 9

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

Accepted Answer

$x = 4$

Answer

$x = 2$

Answer

$x = 6$

Answer

$x = 8$

Question 10

Compute $\log_{10} 1000 + \log_{10} 0.01$.

Accepted Answer

$1$

Answer

$0$

Answer

$2$

Answer

$5$

Logarithm properties — quick reference