# How do you solve 16^(n-7)+5=24?

Sep 4, 2016

$n = 8.06198$

#### Explanation:

Isolate the term with the variable.

${16}^{n - 7} = 19$

19 is clearly not an exact power of 16.
The variable is in the index, so use logs.

$\log {16}^{n - 7} = \log 19$

$\left(n - 7\right) \log 16 = \log 19$

$\left(n - 7\right) = \log \frac{19}{\log} 16$

$n - 7 = 1.06198$

$n = 8.06198$