# How do you calculate log _24 356?

Jun 22, 2016

1.849

#### Explanation:

Use the change of base law:

${\log}_{24} 356 = \frac{\log 356}{\log 24}$

This is calculated on a calculator to give: 1.849

The same result can be obtained from using index form first:

Let ${\log}_{24} 356 = x$

${24}^{x} = 356$

$\log {24}^{x} = \log 356$

$x \log 24 = 356$

$x = \frac{\log 356}{\log 24} = 1.849$