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.
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.