<s>[INST] Find $x$ such that $ 2^{16^x} = 16^{2^x} $. Find $x$ such that $ 2^{16^x} = 16^{2^x}.$
I am a bit confused, what will happen when we expand $16^{2^x}$, will we get  $4^{2^{2^x}}$ or $4^{2^{x+1}}$ ?
 [/INST] See that $2^{16^x} = 16^{2^x}$ is $2^{2^{4x}} = 2^{2^{x+2}}$
then $4x = x + 2$ and get $x = 2/3$.
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