solve 2^3^x = 4.2^5^x

Answer 1

I interpret the powers from right to left, as is the usual convention. This translates the problem to:

2^(3^x) = 4.2^(5^x)

This is essentially an algebra problem.

take log on both sides,
(3^x) log(2) = (5^x) log(4.2)
Rearranging,
(3/5)^x = log(4.2)/log(2)
Take log again,
x log(3/5) = log(log(4.2)/log(2))
solving for x

x = log(log(4.2)/log(2)) / log(3/5)

The numerical value should be around -1.4