# How do you calculate log_5 310?

Sep 1, 2016

$x = 3.564$

#### Explanation:

${\log}_{5} 310 = x$

Change to index form.

${5}^{x} = 310 \leftarrow$ variable is in the index log both sides.

$\log {5}^{x} = \log 310$

$x \log 5 = \log 310$

$x = \log \frac{310}{\log} 5$

Using a calculator or tables gives:

#x = 3.564

Using the "Change of base law" gives the same result.

${\log}_{a} b = \frac{\log b}{\log a}$