Suppose I have a series like
$P\sim A+\epsilon B\,lnM+O(\epsilon ^{2})$
and I want to express it into a power law form. The answer is
$P\sim AM^{\epsilon B/A}+O(\epsilon ^{2})$.
Another example. The expression
$Nl\left \{ 1+\frac{\epsilon }{8}\left [ -1+ln\left ( \frac{2\pi N}{L} \right ) \right ] \right \}$
can be written into the following power law form:
$Nl\left ( 1-\frac{\epsilon }{8} \right )\left ( \frac{2\pi N}{L} \right )^{\frac{\epsilon }{8}}$
The problem is I am not getting how to go from step 1 to step 2.
Can somebody provide me with an explanation?