# How do you calculate ln(4096)/ln(4)?

Jun 9, 2016

$6$

#### Explanation:

$\ln \frac{4096}{\ln} \left(4\right) = \ln \frac{{4}^{6}}{\ln} \left(4\right) = \frac{6 \textcolor{red}{\cancel{\textcolor{b l a c k}{\ln \left(4\right)}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{\ln \left(4\right)}}}} = 6$

Alternatively, use the change of base formula:

${\log}_{a} b = \frac{{\log}_{c} b}{{\log}_{c} a}$

to find:

$\ln \frac{4096}{\ln} \left(4\right) = {\log}_{4} 4096 = {\log}_{4} {4}^{6} = 6$