Answer
$x=3$
Work Step by Step
The given equation is
$\Rightarrow 2^{4x}=2^{x+9}$
Equate the exponents.
$\Rightarrow 4x=x+9$
Subtract $x$ from each side.
$\Rightarrow 4x-x=x+9-x$
Simplify.
$\Rightarrow 3x=9$
Divide each side by $3$.
$\Rightarrow \frac{3x}{3}=\frac{9}{3}$
Simplify.
$\Rightarrow x=3$
Check: $(x=3)$
$\Rightarrow 2^{4(3)}=2^{3+9}$
$\Rightarrow 2^{12}=2^{12}$
True.
Hence, the solution is $x=3$.
