# How do you use the properties of logarithms to rewrite(contract) each logarithmic expression 2log_2(64) + log_2(2)?

Jul 19, 2015

Use ${\log}_{a} \left({a}^{b}\right) = b$ to find:

$2 {\log}_{2} \left(64\right) + {\log}_{2} \left(2\right) = 2 \cdot 6 + 1 = 13$

#### Explanation:

${\log}_{a} \left({a}^{b}\right) = b$, so

$64 = {2}^{6}$ so ${\log}_{2} \left(64\right) = {\log}_{2} \left({2}^{6}\right) = 6$

$2 = {2}^{1}$ so ${\log}_{2} \left(2\right) = {\log}_{2} \left({2}^{1}\right) = 1$

So $2 {\log}_{2} \left(64\right) + {\log}_{2} \left(2\right) = 2 \cdot 6 + 1 = 13$