Question

How do you calculate $\frac{\ln \left(4096\right)}{\ln \left(4\right)}$?

Answer 1

$6$
$\frac{\ln \left(4096\right)}{\ln \left(4\right)}=\frac{\ln \left(4^6\right)}{\ln \left(4\right)}=\frac{6\ln \left(4\right)}{\ln \left(4\right)}=6$
Alternatively, use the change of base formula:
${\log }_{a}b=\frac{{\log }_{c}b}{{\log }_{c}a}$
to find:
$\frac{\ln \left(4096\right)}{\ln \left(4\right)}={\log }_{4}4096={\log }_4{4}^6=6$