324x-1 = 163x

32 = 4·8 = (2·2)·(2·4) = (2·2)·(2·2·2) = 2·2·2·2·2 = 25

16 = 4·4 = (2·2)·(2·2) = 2·2·2·2 = 24

So we replace 32 with (25) and 16 with (24):

(25)4x-1 = (24)3x

We remove the parentheses by multiplying the exponents:

220x-5 = 212x

Since the bases are the same on both sides, and they are positive and
not equal to 1, we can set the exponents equal to each other:

20x - 5 = 12x
     8x = 5
      x = 

Edwin