jmc

We rewrite the left side $16^{16}+16^{16}+16^{16}+16^{16}$ as $4\cdot 16^{16}=2^2\cdot (2^4{)}^{16}=2^2\cdot 2^{64}=2^{66}$. We have $2^{66}=2^x$, so the value of $x$ is $\boxed{66}$.