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Math Help - Help find derivative of y with respect to variable

  1. #1
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    Help find derivative of y with respect to variable

    I have a problem which says

    Y= 3^log(base2)t

    I set it up as

    ln y = log(base2)t (ln 3)

    I am not sure what to do after this step!
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  2. #2
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    Quote Originally Posted by KarlosK View Post
    I have a problem which says

    Y= 3^log(base2)t

    I set it up as

    ln y = log(base2)t (ln 3)

    I am not sure what to do after this step!
    Use the identity \log_a x = \frac{\ln x}{\ln a}.
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  3. #3
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    Quote Originally Posted by KarlosK View Post
    I have a problem which says

    Y= 3^log(base2)t

    I set it up as

    ln y = log(base2)t (ln 3)

    I am not sure what to do after this step!
    \ln y = \log_2 (t) \cdot \ln(3)

    You can differentiate implictly given that \frac{d}{dx} \ln (y) = \frac{1}{y} \cdot \frac{dy}{dx}

    You will also need to use the change of base rule on \log_2 (t)
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