<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] Alternative approach
$$16^{2^x} = [2^4]^{2^x} = 2^{4 \times 2^x}.$$
Since this is equal to $2^{16^x}$ you have
$$16^x = 4 \times 2^x \implies 8^x = 4 \implies x = (2/3).$$
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