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Homework Help: How do I solve for x in this log equation?

  1. Jan 4, 2010 #1
    1. The problem statement, all variables and given/known data
    0.5log(2x-1)+log[tex]\sqrt{x-9}[/tex]=1


    2. Relevant equations
    N/A


    3. The attempt at a solution
    I have no idea how to approach this.
     
  2. jcsd
  3. Jan 4, 2010 #2
    use this laws:
    alogb=[tex]logb^{a}[/tex]
    logm+logn=logmn
     
  4. Jan 4, 2010 #3
    first, rewrite the square root as an exponent, and rewrite 1 as log(10), so you get

    0.5log(2x-1) + log(x-9)^(1/2) = log(10)

    Bring the exponent down to get 0.5log(x-9)

    0.5log(2x-1) + 0.5log(x-9) = log(10)

    multiply both sides by 2

    log(2x-1) + log(x-9) = 2log(10)

    Raise the 10 in the log function to the 2 (100) and multiply the two inner log functions

    log[(2x-1)(x-9)] = log(100)

    take the antilog of both sides and solve for x

    (2x-1)(x-9) = 100

    2x^2 - 19x - 91

    X=13
    X= -3.5
     
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