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Resolution of a logarithmic function

  1. Jan 18, 2009 #1
    1. The problem statement, all variables and given/known data
    Resolve the following equation:
    log2 x + log2 [(x-3)/5)] = 3

    2. Relevant equations
    Logarithmic laws:
    logc m + logc n = logc mn

    3. The attempt at a solution
    Restriction:

    (x-3)/5 > 0
    x-3 > 0
    x > 3

    Resolution:

    log2 x + log2 [(x-3)/5)] = 3
    log2 x[(x-3)/5)] = 3
    log2 [(x2 - 3x)/5x] = 3

    23 = (x2 - 3x)/5x
    8 = (x2 - 3x)/5x
    8(5x) = x2 - 3x
    40x = x2 - 3x
    40x + 3x = x2
    43x = x2
    43 = x2 / x
    43 = x

    My answer book says the answer is 8 however I don't seem to get to that after numerous attempts.

    Thank you in advanced.
     
    Last edited: Jan 18, 2009
  2. jcsd
  3. Jan 18, 2009 #2

    Mark44

    Staff: Mentor

    The next line has an error. The denominator should be 5, not 5x.
     
  4. Jan 18, 2009 #3
    Woops! It should have been 5x if it was x/x but it's x/1.

    Thank you very much again. :)
     
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