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Math Help - Exponents & Radicals

  1. #1
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    Question Exponents & Radicals

    If

    2^x/(1+2^x) = 1/4

    how do I find the value of

    8^x/(1+8^x)?

    Thanks,

    Ron
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  2. #2
    A Plied Mathematician
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    That's a fun little problem. Try this:

    2^{x}=\dfrac{1}{4}(1+2^{x})

    \dfrac{3}{4}\,2^{x}=\dfrac{1}{4}

    3\cdot 2^{x}=1

    2^{x}=\dfrac{1}{3}=\left(8^{1/3}\right)^{x}.

    Raise both sides to the power 3 to obtain

    8^{x}=\dfrac{1}{27}.

    Plug this into the desired expression.
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