how?

2^{2x - 3}  = 32

The trick here is to equate bases

Note that 32  = 2⁵     .....so.....

2^{2x - 3}  =  2⁵          since the bases are the same we can solve for the exponents

2x  - 3   = 5          add 3 to both sides

2x  = 8                divide both sides by 2

x  = 4