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Math Help - How to solve equation contain logarithm

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    23

    How to solve equation contain logarithm

    How to solve this equation:

    4827/t +7log_10(t)-27=0

    please help me
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  2. #2
    Super Member
    Joined
    Aug 2008
    Posts
    903
    Hy. You can solve it by using the Lambert-W function by first writing it as:

    \frac{4827}{t}+7\log_{10} t=27

    \frac{4827}{t}+\frac{7}{\ln(10)}\ln(t)=27

    or just look at:

    \frac{a}{t}+b\ln(t)=c

    Now, in order to get it into a form to use W, you need to put it in the form:

    k=f(t)e^{f(t)}

    then taking W I get:

    f(t)=W(k)

    So try and do some algebra to get:

    -\frac{a}{b}e^{-c/b}=-\frac{a}{bt}e^{-\frac{a}{bt}}

    then take W right?
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