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Math Help - Differentiating natural logarithms

  1. #1
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    Differentiating natural logarithms

    The question is 2x log(base4)x

    I believe this is product rule so I did this:

    2/(ln4) + 2log(base4)x
    or 2/(ln4) + log(base4)x^2

    The answers give (1+lnx)1/ln2

    Did I make a mistake or is that a simplification or..?
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  2. #2
    Super Member
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    Oct 2007
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    London / Cambridge
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    Your answer 2/(ln4) + 2log(base4)x is correct.

    it may be useful to write it like this \frac{2}{\ln{4}}+ \frac{2 \ln{x}}{\ln{4}}

    then use the power law \ln4 = 2 \ln 2

    so giving \frac{1}{\ln 2}+ \frac{ \ln x}{ \ln 2}

    \Rightarrow \frac{1+\ln x}{\ln 2}
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