Answer
$x=\frac{1}{2}(\frac{log(6)}{log(3)-1})\approx.3155$
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.
$3^{2x+1}=6$
Take the common logarithm of both sides (which has base 10).
$log(3^{2x+1})=log(6)$
Use the power property of logarithms.
$(2x+1) log(3)=log(6)$
Divide both sides by $log(3)$.
$2x+1=\frac{log(6)}{log(3)}$
Subtract 1 from both sides.
$2x=\frac{log(6)}{log(3)}-1$
Divide both sides by 2.
$x=\frac{1}{2}(\frac{log(6)}{log(3)-1})\approx.3155$
