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Math Help - Solving for unknown - natural log involved

  1. #1
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    Solving for unknown - natural log involved

    Hello.

    I am a bit rusty on my natural log rules. How would I go about solving for x:

    .25ln(11000 + x) + .75ln(10000 + x) = .25ln(11000) + .75ln(10000)

    Any help would be greatly appreciated.
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  2. #2
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    If you had a\ln (b + x) + c\ln (d + x) = a\ln (b) + c\ln (d) then it follows that:
    \begin{gathered}<br />
  \ln \left[ {(b + x)^a (d + x)^c } \right] = \ln \left[ {(b)^a (d)^c } \right] \hfill \\<br />
  (b + x)^a (d + x)^c  = (b)^a (d)^c  \hfill \\ <br />
\end{gathered}  .
    That at least get it down to xs.
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