# How do you solve  11 ^n − 8 − 5 = 54 ?

Aug 10, 2015

$n = \ln \frac{67}{\ln} \left(11\right)$

#### Explanation:

${11}^{n} - 8 - 5 = 54$
${11}^{n} = 67$
$\ln \left({11}^{n}\right) = \ln \left(67\right)$
$n \cdot \ln \left(11\right) = \ln \left(67\right)$

Therefore,

$n = \ln \frac{67}{\ln} \left(11\right)$