# How do you solve 9^(4x+1)=64?

Mar 9, 2018

$x = 0.223 \ldots$

#### Explanation:

Apply log to both sides and then expand the brackets.

$\left(4 x + 1\right) \log 9 = \log 64$
$4 x \log + \log 9 = \log 64$

minus $\log + 9$ from both sides, then divide by $\log 9$

$4 x \log 9 = \log 64 - \log 9$

$4 x = \frac{\log 64 - \log 9}{\log} 9$

$4 x = 0.8927 \ldots$
$x = 0.223 \ldots$

Check the solution by subbing in the value for $x$

9^(4(0.223...)+1$= 64$
$64 = 64$