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Math Help - Quotient Rule Involving A Logarithm

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    Quotient Rule Involving A Logarithm

    The problem is: g(x) = \frac{10\log_{4} x}{x}

    By doing the quotient rule I get: u = 10\log_{4} x and u' = \frac{10}{ln 4\times{x}} and v = x and v' = 1

    When I apply the quotient rule I get: g'(x) = (10 - ln 4 log_4 x)/(x^2 ln 4) (sorry, I couldn't figure out the latex for this part.)

    This answer is not even remotely close to the actual answer in the book. What did I do wrong?
    Last edited by Bashyboy; May 5th 2012 at 03:46 PM.
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    Re: Quotient Rule Involving A Logarithm

    Quote Originally Posted by Bashyboy View Post
    The problem is: g(x) = \frac{10\log_{4} x}{x}

    By doing the quotient rule I get: u = 10\log_{4} x and u' = \frac{10}{ln 4\times{x}} and v = x and v' = 1

    When I apply the quotient rule I get: g'(x) = (10 - ln 4 log_4 x)/(x^2 ln 4) (sorry, I couldn't figure out the latex for this part.)

    This answer is not even remotely close to the actual answer in the book. What did I do wrong?
    note the change of base formula ...

    \log_b{a} = \frac{\ln{a}}{\ln{b}}


    g(x) = \frac{10\log_{4} x}{x} = \frac{10}{\ln{4}} \cdot \frac{\ln{x}}{x}

    g'(x) = \frac{10}{\ln{4}} \cdot \frac{1 - \ln{x}}{x^2}
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