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Math Help - I dont know how to simplify this logarithm

  1. #1
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    I dont know how to simplify this logarithm

    I am unsure how to simplify this expression, would someone be able to help me out pleeeaasssseee




    2^(log8 7)


    it is log base 8, i just was unsure how to change the font size

    thank you
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  2. #2
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    Quote Originally Posted by burdonjo View Post
    I am unsure how to simplify this expression, would someone be able to help me out pleeeaasssseee




    2^(log8 7)


    it is log base 8, i just was unsure how to change the font size

    thank you
    Maybe you know that 8^{\frac13} = 2

    2^{\log_8 7} = \left(8^{\frac13} \right)^{\log_8 7} = \left(8^{\log_8 7} \right)^{\frac13} = 7^{\frac13} = \sqrt[3]{7}
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  3. #3
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    Hello,l burdonjo!

    There are a number of approaches.
    Here's mine . . .


    Simplify: . 2^{\log_87}

    We have: . 2^{\log_87} \;=\;\left(8^{\frac{1}{3}}\right)^{\log_87} \;=\;(8)^{\frac{1}{3}\log_87} \;=\;(8)^{\log_8\left(7^{\frac{1}{3}}\right)}\;=\;  7^{\frac{1}{3}} \;=\;\sqrt[3]{7}


    Edit: Too fast for me, E.B.
    .
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