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Math Help - Simplifying natural logarithm

  1. #1
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    Simplifying natural logarithm

    Trying to simplify the derivative of this to find a constant,

    y = ln[{lnx/A}/{1-[lnx/A]}]

    The best I can is get to

    y'=ln[lnx/{A-lnx}]

    Any ideas?
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Ok here is what you do

    Quote Originally Posted by theowne View Post
    Trying to simplify this to get a constant rather than a variable...

    y = ln[{lnx/A}/{1-[lnx/A]}]

    The best I can is get to

    y=ln[lnx/{A-lnx}]

    Any ideas?
    \ln\bigg[\frac{\frac{\ln(x)}{A}}{1-\frac{\ln(x)}{A}}\bigg]...and using the rules you can get it to ln\bigg[\frac{\ln(x)}{A}\bigg]-\ln\bigg[1-\frac{\ln(x)}{A}\bigg]...so you can then go ln(ln(x))-ln(A)-ln\bigg[\frac{1}{A}\bigg[A-\ln(x)\bigg]\bigg]
    which goes to ln(ln(x))-ln(A)+ln(A)+ln[A-ln(x)]... ln(ln(x))-ln[A-ln(x)]
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