Answer
$$
16^{x+3} =64^{2 x-5}
$$
The solution of the given equation is
$$
x=\frac{21}{4}.
$$
Work Step by Step
$$
16^{x+3} =64^{2 x-5}
$$
Since the bases must be the same, write 16 as $2^{2 }$ and 64 as $ 2^{6} $ giving
$$
\begin{aligned} 16^{x+3} &=64^{2 x-5} \\\left(2^{4}\right)^{x+3} &=\left(2^{6}\right)^{2 x-5} \\ 2^{4 x+12} &=2^{12 x-30} \\ 4 x+12 &=12 x-30 \\ 42 &=8 x \\ \frac{21}{4} &=x \end{aligned}
$$
So, the solution of the given equation is
$$
x=\frac{21}{4}.
$$
