Could someone please explain this for me?
Solve the equation: log(2x - 3) = log(3 - x) - 2.
Before we start:
2x-3 > 0 ----> x> 1.5 and 3-x>0 --> x < 3
so 1.5 < x < 3
log(2x - 3) = log(3 - x) - 2
log(2x - 3) - log(3 - x) = - 2
log( (2x-3)/(3-x)) = -2
by definition
(2x-3)/(3-x) = 10^-2 = 1/100
200x - 300 = 3-x
201x = 303
x = 303/201 = 101/67 = appr 1.5075
which does fall within our permissible domain