# What is the base conversion formula for logarithms?

${\log}_{a} \left(x\right) = \frac{{\log}_{b} \left(x\right)}{{\log}_{b} \left(a\right)}$
${\log}_{10} \left(100\right) = \frac{{\log}_{e} \left(100\right)}{{\log}_{e} \left(10\right)} = \frac{\ln \left(100\right)}{\ln \left(10\right)} = 2$