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.

2. If you had $\displaystyle a\ln (b + x) + c\ln (d + x) = a\ln (b) + c\ln (d)$ then it follows that:
$\displaystyle \begin{gathered} \ln \left[ {(b + x)^a (d + x)^c } \right] = \ln \left[ {(b)^a (d)^c } \right] \hfill \\ (b + x)^a (d + x)^c = (b)^a (d)^c \hfill \\ \end{gathered}$.
That at least get it down to x’s.