Solve for x: log(2) x = log(8) 256

For any system of logarithms we can use the relation: log
(a) b = log(x) a / log(x) b where x can be any positive number to be use as the
base.

Now using x= 2,

log (8)
256 = log(2) 256 / log(2) 8.

But we know that log(2) 8
=3

Also log (2) 256 = 8

So
log(2) 256 / log(2) 8 = 8/3

Or log(2) x =
8/3

Raising both sides to the power 2, we
get

x =
2^(8/3)

Therefore x =
2^(8/3)