Answer
$x=4$
Work Step by Step
We are given the equation $9^{2x-8}=27^{x-4}$. First, we must write both sides using the same base.
$((3)^{2})^{2x-8}=3^{4x-16}$
$((3)^{3})^{x-4}=3^{3x-12}$
So, $3^{4x-16}=3^{3x-12}$.
Next, we must take the natural log of both sides.
$ln(3^{4x-16})=ln(3^{3x-12})$
$(4x-16)ln(3)=(3x-12)ln(3)$
Divide both sides by $ln(3)$.
$4x-16=3x-12$
Subtract $3x$ from both sides.
$x-16=-12$
Add 16 to both sides.
$x=4$
