# How do you express log_5 20 in terms of common logarithms?

Dec 20, 2016

${\log}_{5} 20 = \log \frac{20}{\log} 5$

#### Explanation:

let$\text{ } y = {\log}_{5} 20$

$\implies {5}^{y} = 20$

take logs to base 10 on both sides

$\log {5}^{y} = \log 20$

$y \log 5 = \log 20$

$y = {\log}_{5} 20 = \log \frac{20}{\log} 5$