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Math Help - LOGS

  1. #1
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    LOGS

    Find f'(x)
    e) f(x) 2^(log(3)x)

    The 3 is subscript

    Guys this is the last problem for my homework help me through this
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  2. #2
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    Which rule would you use first
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  3. #3
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    the problem is f(x) = 2^(log(3) x)
    sorry about that
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  4. #4
    Member
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    Acolman, Mexico
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    So you have something like this

    y=2^{(\log {3})x} and you want to find y'



    \log {y}=\log {(2^{(\log {3})x})}=(\log{2})(\log {3})x
    Now differentiate both sides
    \frac{1}{y} y'=(\log{2})(\log {3})
     y'=(\log{2})(\log {3})y=(\log{2})(\log {3})2^{(\log {3})x}
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  5. #5
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    Lexington, MA (USA)
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    Hello, bigton!

    We're expected to know these two formulas:

    . . f(x) \:=\:b^u \quad\Rightarrow\quad f'(x) \:=\:b^u\,u'\ln(b)

    . . f(x) \:=\:\log_b(u) \quad\Rightarrow\quad f'(x) \:=\:\frac{1}{u\ln(b)}



    Find f'(x)\!:\;\;f(x) \:=\:2^{\log_3(x)}

    f'(x) \;=\;2^{\log_3(x)}\cdot\frac{1}{x\ln(3)}\ln(2) \;=\;\frac{2^{\log_3(x)}\ln(2)}{x\ln(3)}

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