# How do you calculate log_6 53 with a calculator?

Aug 19, 2016

$x = 2.216$

#### Explanation:

Some calculators can do log calculations with bases other than 10.
However, let's assume that we have a calculator which only has log with base 10.

Let ${\log}_{6} 53 = x \text{ write in index form}$

${6}^{x} = 53 \text{ find log of both sides}$

$\log {6}^{x} = \log 53$

$x \log 6 = \log 53$

$x = {\log}_{10} \frac{53}{\log} _ 10 6$

This is the same result as using the change of base rule.

$x = 2.216$