# How do you evaluate log_3 18?

May 19, 2016

$= {\log}_{3} \left(9 \times 2\right)$

$= {\log}_{3} \left(9\right) + {\log}_{3} \left(2\right)$

$= \log \frac{9}{\log} 3 + \log \frac{2}{\log} 3$

$= \log {3}^{2} / \log 3 + \log \frac{2}{\log} 3$

$= 2 \frac{\cancel{\log 3}}{\cancel{\log 3}} + \log \frac{2}{\log} 3$

$= 2 + {\log}_{3} \left(2\right)$

Hopefully this helps!