Answer
$x=3$
Work Step by Step
The given equation is
$\Rightarrow 64^{2x+4}=16^{5x}$
Rewrite $64$ as $4^3$ and $16$ as $4^2$.
$\Rightarrow (4^3)^{2x+4}=(4^2)^{5x}$
Use $(a^n)^m=a^{n\cdot m}$
$\Rightarrow 4^{3(2x+4)}=4^{2(5x)}$
Simplify.
$\Rightarrow 4^{6x+12}=4^{10x}$
Equate the exponents.
$\Rightarrow 6x+12=10x$
Subtract $6x$ from each side.
$\Rightarrow 6x+12-6x=10x-6x$
Simplify.
$\Rightarrow 12=4x$
Divide each side by $4$.
$\Rightarrow \frac{12}{4}=\frac{4x}{4}$
Simplify.
$\Rightarrow 3=x$
Check: $(x=3)$
$\Rightarrow 64^{2x+4}=16^{5x}$
$\Rightarrow 64^{2(3)+4}=16^{5(3)}$
$\Rightarrow 64^{6+4}=16^{15}$
$\Rightarrow 64^{10}=16^{15}$
$\Rightarrow 1.1529215e+18=1.1529215e+18$
True.
Hence, the solution is $x=3$.
