Answer
$x=7$
Work Step by Step
We are given the exponential equation $8^{x+3}=16^{x-1}$.
We can express each side using a common base and then solve for $x$.
$8^{x+3}=(2^{3})^{x+1}=2^{3x+3}$
$16^{x-1}=(2^{4})^{x-1}=2^{4x-4}$
$2^{3x+3}=2^{4x-4}$
Take the natural log of both sides.
$ln(2^{3x+3})=ln(2^{4x-4})$
$(3x+3)ln(2)=(4x-4)ln(2)$
Divide both sides by $ln(2)$.
$3x+3=4x-4$
Subtract $3x$ from both sides.
$3=x-4$
Add 4 to both sides.
$x=7$
