# How do you solve 2^(5n-5)+2=75?

Sep 12, 2016

${2}^{5 n - 5} = 73$

$\log \left({2}^{5 n - 5}\right) = \log 73$

$\left(5 n - 5\right) \log 2 = \log 73$

$5 n \log 2 - 5 \log 2 = \log 73$

$5 n \log 2 = \log 73 + \log 32$

$n = \log \frac{2336}{\log} 32$

The decimal approximation will be $n \cong 2.24$.

Hopefully this helps!