# How do you evaluate log_3 (1/243)?

Oct 1, 2016

${\log}_{3} \left(\frac{1}{243}\right) = {\log}_{3} {3}^{-} 5 = - 5$

#### Explanation:

Logs and exponential equations become much easier to understand if you know the powers up to 1,00.

Note that $243 = {3}^{5}$

${\log}_{3} \left(\frac{1}{243}\right)$ is asking the question..

$\text{What index of 3 gives } \frac{1}{243}$?

$\frac{1}{243} \text{ is which power of } 3$?

$\frac{1}{243} = \frac{1}{3} ^ 5 = {3}^{-} 5 \text{ } \leftarrow$ here is our answer!

${\log}_{3} \left(\frac{1}{243}\right) = {\log}_{3} {3}^{-} 5 = - 5$