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Math Help - Logarithmic Function - Performance Problem

  1. #1
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    Logarithmic Function - Performance Problem

    Been having trouble with this one, any help would be appreciated.

    Log2x + Log4x = 5 (both the 2 and the 4 are subscripts)

    So wouldn't you put it into exponential form and then solve for the trinomial?
    So it would be like 2^2x +2^x-5=0 and then let a variable = 2^x?
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  2. #2
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    Quote Originally Posted by peekay View Post
    Been having trouble with this one, any help would be appreciated.

    Log2x + Log4x = 5 (both the 2 and the 4 are subscripts)

    So wouldn't you put it into exponential form and then solve for the trinomial?
    So it would be like 2^2x +2^x-5=0 and then let a variable = 2^x?
    From the change base formula you know:

    \log_4(x)=\dfrac{\ln(x)}{\ln(4)}=\dfrac{\ln(x)}{2 \ln(2)}=\dfrac12 \log_2(x)

    Therefore the given equation becomes:

    \log_2(x)+\dfrac12 \log_2(x)=5~\implies~\log_2(x)=\dfrac{10}3~\implie  s~\boxed{x=2^{\frac{10}3} = \sqrt[3]{1024}}
    Last edited by earboth; May 5th 2009 at 01:45 AM.
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