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Math Help - Solving simple logarithmic equations

  1. #1
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    Solving simple logarithmic equations

    I missed a whole week of math class and I'm totally lost. I learn best through examples and working my way back from answers through trial and error.

    how would I solve for logx16 = 2/3 (with x being the base)... I rewrote it as X^2/3 = 16 but don't know where to go from there... Thanks in advance, I'm sure this is a really simple answer.

    And, log(base x)(1/81)=-4
    Last edited by Huggakhan; December 16th 2012 at 12:59 PM.
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  2. #2
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    Re: Solving simple logarithmic equations

    So far so good.
    Now remove the fractional power by raising both sides to the power three and then taking square roots.
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  3. #3
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    Re: Solving simple logarithmic equations

    Yes, I did that and I got the answer.

    For the next one I also got the answer, but I don't know if my process is correct.
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  4. #4
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    Re: Solving simple logarithmic equations

    Best is to use the rule

    \displaystyle \log\left(\frac{a}{b}\right)=\log a - \log b, which works for any base.

    Simplify what you get and then use the same process as for the first one.
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  5. #5
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    Re: Solving simple logarithmic equations

    Quote Originally Posted by Huggakhan View Post
    I missed a whole week of math class and I'm totally lost. I learn best through examples and working my way back from answers through trial and error.

    how would I solve for logx16 = 2/3 (with x being the base)... I rewrote it as X^2/3 = 16 but don't know where to go from there... Thanks in advance, I'm sure this is a really simple answer.

    And, log(base x)(1/81)=-4
    log Bx (1/81)=-4
    x^-4 = 1/81
    1/x^4 =1/81
    x^4 =81
    x=3
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