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Math Help - Logarithms

  1. #1
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    Logarithms

    Solve.

    (1/4)^x+4 = √8

    x+4 log 1/4= Log √8

    I dont really no what to do from there...
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by Skoz View Post
    Solve.

    (1/4)^x+4 = √8

    x+4 log 1/4= Log √8

    I dont really no what to do from there...
    \left(\frac{1}{4}\right)^{x+4} = \sqrt{8}

    Note that

    \frac{1}{4} = 2^{-2}

    \sqrt{8} = 2\sqrt{2} = 2^{1.5}

    Now you can convert all your numbers into base 2


    2^{-2(x+4)} = 2^{1.5}

    Now if the bases are the same the exponents must also be the same

    -2x-8=1.5

    Solve the linear equation for x

    I get x = -4.75
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  3. #3
    Super Member bigwave's Avatar
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    Quote Originally Posted by Skoz View Post
    Solve.

    (1/4)^x+4 = √8

    x+4 log 1/4= Log √8

    I dont really no what to do from there...
    well what was previously shown is much better way to solve it
    however if you need to solve with logarothms

    \left(x+4\right)\left(log1 - log4\right) = \frac{log8}{2}

     <br />
-xlog4 - 4log4 = \frac{log8}{2}<br />

     <br />
-xlog4 = \frac{log8 + 8log4}{2log4} = -4.75<br />

    have assumed some of the steps
    Last edited by bigwave; December 16th 2009 at 01:42 PM. Reason: wording
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