Question

Find x if 2^16^x = 16^2^x

Just to make this clear, if you were reading this aloud, it would sound like this:

if 2 to the power of 16 to the power of x equals 16 to the power of 2 to the power of x.

So basically, the x would not be the same size as the 2 or 16, but really tiny and above the 2 and 16.

Thank you!

Answer 1

(2^16)^x = (16^2)^x
16^2^x = [(2^4)^2]^x
and
a^b^c = a^(bc)
so
2^16 x = 2^8x
16 x log 2 = 8 x log 2
16 x = 8 x ?
not unless x = 0