2 ^(16^x) = 16^(2^x) take the log of each side
log 2 ^(16^x) = log 16^(2^x) and we can write
(16^x) log 2 = (2^x) log 16
(16^x) / (2^x) = log 16/log 2
(16/2)^x = log 16/log 2
8^x = log 2^4 / log 2
8^x = (4log 2) / log 2
8^x = 4
(2^3)^x = 2^2
2^(3x) = 2^2 equate exponents
3x = 2
x = 2/3