#### Answer

$x=\frac{1}{3}(\frac{log(9)}{log(4)}-2)\approx-.1383$

#### Work Step by Step

According to the logarithm property of equality $log_{b}a=log_{b}c$ is equivalent to $a=c$ (where a, b, and c are real numbers such that $log_{b}a$ and $log_{b}c$ are real numbers and $b\ne1$). We can use this property to solve for x.
$4^{3x+2}=9$
Take the common logarithm of both sides (which has base 10).
$log(4^{3x+2})=log(9)$
Use the power property of logarithms.
$(3x+2) log(4)=log(9)$
Divide both sides by $log(4)$.
$3x+2=\frac{log(9)}{log(4)}$
Subtract 2 from both sides.
$3x=\frac{log(9)}{log(4)}-2$
Divide both sides by 3.
$x=\frac{1}{3}(\frac{log(9)}{log(4)}-2)\approx-.1383$