Hello,
I assume that your problem reads:
4^(2x+1) * 5^(x-2) = 6^(1-x)
Expand the powers:
4*(4^2)^x * 5^x / 25 = 6 / (6^x)
Rearrange so that all constant numbers are at the RHS of the equation:
16^x * 5^x * 6^x = (6 * 25)/4
(480)^x = 150/4
x is the logarithm of 150/4 to the base of 480:
x = [log(150/4)] / (log(480)] ≈ 0.587053207...
tschüss
EB