Error in Srednicki renormalization?

[Higgsy]

On page 164-165 of srednicki's printed version (chapter 27) on other renormalization schemes, he arrives at the equation $$m_{ph}^{2} = m^2 \left [1 \left ( +\frac{5}{12}\alpha(ln \frac{\mu^2}{m^2}) +c' \right ) + O(\alpha^2)\right]$$

But after taking a log and dividing by 2 he arrives at
$$ln[m_{ph}] = ln[m] \left [ \left ( \frac{5}{12}\alpha(ln \frac{\mu}{m}) +\frac{1}{2} c' \right ) + O(\alpha^2)\right]$$

Why is there no ln on the $$\frac{5}{12} \alpha$$ term?

 

[The_Duck]

He is using the relation
\ln(1 + x) = x + O(x^2)
Here $x$ has an $\alpha$ in it, so the $O(x^2)$ term is absorbed into the $O(\alpha^2)$.

 

[Higgsy]

Thanks!