# How do you evaluate log_5(1/2)?

May 2, 2016

By calculator -0.431 (3 dec places)

#### Explanation:

Let ${\log}_{5} \left(\frac{1}{2}\right) = x$

Change from log form to index from: ${5}^{x} = \frac{1}{2}$

Now, because the variable is the index, and $\frac{1}{2}$ is not an exact power of 5, we need to use logs.

Power law: $x \log 5$ = log 0.5)

$x = \frac{\log 0.5}{\log 5}$

From a calculator $x$ = -0.431