# How do you evaluate log_4(1/4)?

Dec 29, 2015

$- 1$

#### Explanation:

The logarithm of the p-th power of a number is p times the logarithm of the number itself:

$\textcolor{w h i t e}{\times} {\log}_{4} \left(\frac{1}{4}\right) = {\log}_{4} \left({4}^{-} 1\right)$
$\textcolor{w h i t e}{\times \times \times \times} = \textcolor{red}{- 1} \times {\log}_{4} 4$
$\textcolor{w h i t e}{\times \times \times \times} = - 1$

graph{logx/log4 [-10, 10, -5, 5]}
Graph of ${\log}_{4} x$