# How do you solve 4^(5n)>30?

May 19, 2018

$n > 0.49$

#### Explanation:

By rules of logarithms:

$\ln {a}^{b} = b \ln a$

Therefore, take the logarithm from both sides of the function and follow the rule. Then proceed to rearrange and simplify to find the solution for $n$.

$\ln {4}^{5} n > \ln 30$

$5 n \ln 4 > \ln 30$

$5 n > \ln \frac{30}{\ln} 4$

$n > \frac{\ln \frac{30}{\ln} 4}{5}$

$n > 0.49$

Hope this helps!