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Math Help - logarithmic

  1. #1
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    logarithmic

    Given that , what is the value of ?

    Can someone show me how to solve this please? Cheers x
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  2. #2
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    Or you can use the facts that \log_b5^{1/2} = \tfrac12\log_b5 and \log_b5^4 = 4\log_b5. Then the equation simplifies to \log_b5=4, which you should be able to solve on a calculator.
    Last edited by Opalg; November 26th 2008 at 07:40 AM. Reason: Corrected silly mistake (thanks to Mathstud28)
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    -2\log_x(\sqrt{5})+5\log_x(5^4)=76

    Using the change of base theorem

    -2\frac{\frac{1}{2}\ln(5)}{\ln(x)}+20\frac{\ln(5)}{  \ln(x)}=76

    Solving gives

    \ln(x)=\frac{\ln(5)}{4}\implies{x=5^{\frac{1}{4}}}
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Opalg View Post
    Or you can use the facts that \log_b5^{1/2} = \tfrac12\log_b5 and \log_b5^4 = 4\log_b5. Then the equation simplifies to \log_b5=4, which you should be able to solve on a calculator.
    I deleted my original post in this thread after seeing the other replies thinking I had made an awfull mistake, but looking at these replies I see that they are addressing the problem:

    -2 \log_b(5^{1/2})+5\log_b(5^4)=76

    which seems natural enough because it can be solved in close form.

    However that is not my reading of the question, which was to solve:

    -2^{ \log_b(5^{1/2})}+5^{\log_b(5^4)}=76

    which is somewhat different! and I stand by my earlier now deleted post and suggest graphical and/or numerical solution for this.

    There is a real solution is close to b=10.84.

    CB
    Last edited by CaptainBlack; November 27th 2008 at 06:16 AM.
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