Answer
$x=4$
Work Step by Step
The given equation is
$\Rightarrow 3^{9x}=3^{7x+8}$
Equate the exponents.
$\Rightarrow 9x=7x+8$
Subtract $7x$ from each side.
$\Rightarrow 9x-7x=7x+8-7x$
Simplify.
$\Rightarrow 2x=8$
Divide each side by $2$.
$\Rightarrow \frac{2x}{2}=\frac{8}{2}$
Simplify.
$\Rightarrow x=4$
Check: $(x=4)$
$\Rightarrow 3^{9(4)}=3^{7(4)+8}$
$\Rightarrow 3^{36}=3^{28+8}$
$\Rightarrow 3^{36}=3^{36}$
True.
Hence, the solution is $x=4$.
