Answer
True
Work Step by Step
We are given the following expression:
$\log_2{4}+\log_2{8}\stackrel{?}{=}5$
Recall the product property of logarithms (pg. 462):
$\log_b{mn}=\log_b{m}+\log_b{n}$
Applying this property to the left side, we obtain:
$\log_2{4}+\log_2{8}=\log_2{4\cdot8}=\log_2{32}$
Next, recall the power property of logarithms (pg. 462):
$\log_b{m^n}=n\log_b{m}$
We apply this to our last expression:
$\log_2{32}=\log_2{2^5}=5\log_2{2}=5\times 1=5$
We used the fact that $\log_{5}{5}=1$ (because $5^1=5$).
Thus we see that the expression is True.
