Let 4^x-3^ (x-1/2) = 3^ (x+1/2) - 2^ (2x-1) find x=?

4^x-3^ (x-1/2) = 3^ (x+1/2) - 2^ (2x-1)

4^x - 3^x * 3^-1/2 = 3^x * 3^1/2 - 2^2x * 2^-1

2^2x + 2^2x * 1/2 = 3^x * 3^1/2 + 3^x * 3^-1/2

2^2x (1 + 1/2) = 3*x (3^1/2 + 3^-1/2)

3/2 * 2^2x = 2.3094 * 3^x

ln 1.5 + 2x ln 2 = ln 2.3094 + x ln 3

2x ln 2 - x ln3 = ln 2,3094 - ln 1.5

1.3863 x - 1.0986 x = 0.4315

0.2877x = 0.4315

x = 1.5 Answer