4^x - 4^(x - 1) = 24
4^x - 4^x / 4 = 24 multiply through by 4
4 * 4^x - 4^x = 96
3* 4^x = 96 divide both sides by 3
4^x = 32
(2^2)^x = 32
2^(2x) = 32
2^(2x) = 2^5 equate exponents
2x =5
x = 5/2 = 2.5
So
(2x)^x = ( 2 * 2.5)^2.5 = 5^(2.5) = 5^(2 + .5) = 5^2 * 5^.5 = 25√5