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Math Help - derivative of x raise to log

  1. #1
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    derivative of x raise to log

    find dy/dx of


    and answer must be in terms of natural logs

    ok i tried taking the natural log of both sides and i got
    dy/dx= x^log7(x)[ln(x)/xln(7)+log7(x)/x] but I don't know how to get everything in terms of natural log instead of log7(x)
    please help

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  2. #2
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    If y= log_7(x), then x= 7^y= e^{ln(7^y)}= e^{yln(7)}. From that ln(x)= yln(7) so
    y= log_7(x)=  \frac{ln(x)}{ln(7)}.
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  3. #3
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    i keep getting this but its telling me that it isn't the right answer
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  4. #4
    MHF Contributor Unknown008's Avatar
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    I don't know what you did, but remember that ln(7) is a constant.

    How would you differentiate aln(x) ?
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