# How do you express log_7 3 in terms of common logarithms?

Oct 22, 2016

$\implies y = {\log}_{10} \frac{3}{\log} _ \left(10\right) 7$

#### Explanation:

let $y = {\log}_{7} 3$

$\implies {7}^{y} = 3$

Take logs to base 10 both sides

${\log}_{10} {7}^{y} = {\log}_{10} 3$

$\implies y {\log}_{10} 7 = {\log}_{10} 3$

$\implies y = {\log}_{10} \frac{3}{\log} _ \left(10\right) 7$