Answer
$x=7$
Work Step by Step
We are given the equation $16^{2x+1}=64^{x+3}$. First, we must write both sides using the same base.
$((4)^{2})^{2x+1}=4^{4x+2}$
$((4)^{3})^{x+3}=4^{3x+9}$
So, $4^{4x+2}=4^{3x+9}$.
Next, we must take the natural log of both sides.
$ln(4^{4x+2})=ln(4^{3x+9})$
$(4x+2)ln(4)=(3x+9)ln(4)$
Divide both sides by $ln(4)$.
$4x+2=3x+9$
Subtract $3x$ from both sides.
$x+2=9$
Subtract 2 from both sides.
$x=7$
