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Math Help - Logarithmic Help Please

  1. #1
    Junior Member
    Joined
    May 2006
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    Wink Logarithmic Help Please

    I have a few problems I am having difficulty with if someone wouldn't mind helping me please. I am a little confused on how to show these types of problems. I can do a few but these ones are getting to me.
    thank you!!

    First problem:

    Write in logarithmic from

    square root sign only over the #36 then = 6

    Second Problem:

    simplify expression:

    In e^5x

    third problem:

    solve equation:
    3^x-2=81

    & the fourth is the same to solve the equation:

    log x= 1 over2
    25
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  2. #2
    MHF Contributor
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    1. \sqrt{36}=6
    \log_{36}6=\frac{1}{2}

    2. \ln(e^{5x})=5x\ln(e)=5x(1)=5x
    Last edited by Jameson; June 19th 2006 at 09:05 AM.
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  3. #3
    Super Member

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    Hello, kbryant05!

    3) Solve: 3^{x-2} \,= \,81
    With exponential equations, try to get the same base on both sides.

    Since 81 = 3^4, we have: 3^{x-2}\:=\:3^4

    The bases are equal, so the exponents are equal: . x - 2\:=\:4

    Therefore: . x = 6


    4) Solve: \log_{25}x \,= \,\frac{1}{2}
    You should know how to rewrite this in exponential form: . x \:=\:25^{\frac{1}{2}

    Therefore: . x\:=\:\sqrt{25}\:=\:5
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