Here is what i have thus far..

2^(3x-4) -3^(2x+5) = 7

3xlog2 -4log2 +2xlog-3 +5log-3 = 7

3xlog2 +2xlog-3 = 7 + 4log2 -5log-3

3xlog2+ 2xlog-3 = 7 +log256 - log 243

3xlog2+ 2xlog-3 = 7 + log(256/243)

3xlog2+ 2xlog-3 = 8.05

Not sure where to take it from here. Any help is appreciated <3.