# How do you evaluate log_3(1/27)?

Dec 19, 2015

$\textcolor{w h i t e}{\times} - 3$

#### Explanation:

$\textcolor{w h i t e}{\times} {\log}_{3} \left(\frac{1}{27}\right) = {\log}_{3} \left(\frac{1}{3} ^ 3\right)$
$\textcolor{w h i t e}{\times \times \times \times x} = {\log}_{3} {3}^{-} 3$
$\textcolor{w h i t e}{\times \times \times \times x} = - 3 \times {\log}_{3} 3$
(The logarithm of the power of a number rule)

$\textcolor{w h i t e}{\times \times \times \times x} = - 3 \times 1$
$\textcolor{w h i t e}{\times \times \times \times x} = - 3$