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Thread: Using Ln Rules

  1. #1
    MHF Contributor Jason76's Avatar
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    Using Ln Rules

    When you have the opportunity to use \ln rules, then do you always use it? It seems to be the case in Calculus and Diff. Equations.

    For instance, when getting the integrating factor (in Diff. Equations), then you often go from e^{5\ln(b)} =  e^{\ln (b)^{5}} = b^{5} etc...

    In ln differentiation, if you see \ln x^{2} then you make it 2 \ln x
    Last edited by Jason76; Oct 25th 2014 at 10:56 AM.
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  2. #2
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    Re: Using Ln Rules

    Hello, Jason76!

    When you have the opportunity to use \ln rules, then do you always use it?
    It seems to be the case in Calculus and Diff. Equations.
    99% of the time, it is to our advantage to do so.

    For instance, when getting the integrating factor (in Diff. Equations),
    then you often go from e^{5\ln(b)} =  e^{\ln (b)^{5}} = b^{5} etc...
    Of course!

    In ln differentiation, if you see \ln x^{2} then you make it 2 \ln x

    This makes even more sense.

    If we had: y \:=\:\ln(x^4)

    . . pwe can use the Chain Rule: . \frac{dy}{dx} \:=\:\frac{1}{x^4}(4x^3) \:=\: \frac{4}{x}

    Or apply the log rule first: . y \:=\:4\ln(x)

    . . \frac{dy}{dx} \:=\:4\left(\frac{1}{x}\right) \:=\:\frac{4}{x}

    It's your choice.

    Thanks from topsquark
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