# Series expansion in terms of logs [closed]

Say I have

$A = c_1 (Log(a b))^2 + c_2 (Log(a))^2 + c_3 Log(a) + c_4$

Then, I can imagine expansion of terms in term of $Log(a)$:

$A= \{c_4 + c_1 (Log(b))^2\} + Log(a) \{ c_3 +2 c_1 Log(b)\} + (Log(a))^2\{c_1 + c_2\}$

Is there any ways to achieve this in Mathematica when I have a complicated expression in terms of $A$?

• This could be edited into a good self-anwered question. You would have to express both the problem and its answer in the Wolfram Language, not in MathJax. You would also have to give a example of how it would be used in a more complicated expression involving A As it stands, it is likely to be closed. – m_goldberg Jul 27 '17 at 22:07
• We can reopen this if you edit into a proper self-answered question with relevant code. – J. M. will be back soon Jul 28 '17 at 6:44

Let $a = Exp[c],$ then $Log^n[a] = c^n,$ then do series expansion around $c=0$. Then expansion in $c$ is really, expansion in $Log[a]$.

• Applying your procedure to A in the question would make your answer more effective. – bbgodfrey Jul 27 '17 at 16:53
• Yeah, that is what I meant. I was just noting that c is Log[a]. – Quantization Jul 27 '17 at 18:23