Math

Could someone please explain this for me?
Solve the equation: log(2x - 3) = log(3 - x) - 2.

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asked by Smothx
  1. 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

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    posted by Reiny

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