# How do you calculate log _6 (1)?

Jun 20, 2016

${\log}_{6} \left(1\right) = \textcolor{g r e e n}{0}$

#### Explanation:

Remember what $\log$ actually means:
$\textcolor{w h i t e}{\text{XXX}} {\log}_{b} \left(a\right) = \textcolor{red}{c}$ means ${b}^{\textcolor{red}{c}} = a$

In the given case
$\textcolor{w h i t e}{\text{XXX}}$if ${\log}_{6} \left(1\right) = \textcolor{red}{c}$ this means that ${6}^{\textcolor{red}{c}} = 1$

...and since ${6}^{\textcolor{red}{0}} = 1$

${\log}_{6} \left(1\right) = \textcolor{red}{0}$