Let $\log_2 x=2k$ Then the given equation is $2^k=2k$ and by drawing graph, we know that $k=1$ is the only solution(because $y=2^x,y=2x$ are tangent at $x=1$) Hence, $x=4$ is the only solution

golema11 wrote: Let $\log_2 x=2k$ Then the given equation is $2^k=2k$ and by drawing graph, we know that $k=1$ is the only solution(because $y=2^x,y=2x$ are tangent at $x=1$) Hence, $x=4$ is the only solution $\boxed{x=16}$ is also a solution