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Question on logs

  1. Oct 29, 2003 #1
    I need some help on two log questions. I do understand everything of the problem until the final answer, it does not make sense.

    Problem 1:
    log3(x-1)^2 - log3(x^2 -1) = -1 + log3(x-1)

    2log3(x-1) - log3(x^2 -1) = -1 + log3(x-1)

    2log3(x-1) - log3(x-1) - log3(x^2 -1) = -1

    log3(x-1) - log3(x^2 -1) = -1

    log3 x-1/(x-1)(x+1) = -1

    log3 1/x+1 = -1

    =3^-1 = 1/3

    x = 2 <=== why does it equal two?

    Problem 2:
    logx^5 + log x = (log x)(2logx)
    5logx + logx = 2(logx)^2
    6logx = 2(logx)^2
    3 = logx <=== why does it equal 3? How does it turn from 6logx to 3?
    x = 10^3

    Thank you!
     
  2. jcsd
  3. Oct 29, 2003 #2

    Njorl

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    Science Advisor

    Problem 1
    You got a little sloppy with parentheses

    should be

    log3 (x-1)/(x-1)(x+1) = -1

    log3 1/(x+1) = -1

    raise three to the power of each side yields

    1/(x+1)=3^(-1)=1/3

    1/(x+1)=1/3
    x+1=3
    x=2


    Problem 2

    both sides were divided by 2logx

    6logx/2logx=3

    2(logx)^2/2logx=logx

    Njorl
     
  4. Oct 31, 2003 #3
    Thanks buddy.
     
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