Answer
$x=4$
Work Step by Step
Using the laws of exponents, the given equation, $
16^{2x+1}=8^{3x}
,$ is equivalent to
\begin{array}{l}\require{cancel}
(2^4)^{2x+1}=(2^3)^{3x}
\\\\
2^{4(2x+1)}=2^{3(3x)}
.\end{array}
Since the bases are the same, the exponents can be equated. Hence, the solution is
\begin{array}{l}\require{cancel}
4(2x+1)=3(3x)
\\\\
8x+4=9x
\\\\
8x-9x=-4
\\\\
-x=-4
\\\\
x=4
.\end{array}
