# How do you calculate log_4 1558 ?

Jul 6, 2016

Using a calculator: $x = 5.3027$

#### Explanation:

If ${\log}_{4} 1558 = x , \text{ then } {4}^{x} = 1558$

1558 is not a power of 4 (it is not divisible by 4) so use logs.

Take logs of both sides:

$x \log 4 = \log 1558$

$x = \log \frac{1558}{\log} 4$

We would get to the same result from the change of base law.

Using a calculator: $x = 5.3027$