I have:

PowerExpand[Log[Product[f[i], {i, 1, n}]]] // InputForm
(* Output: Log[Product[f[i], {i, 1, n}]] *)

However, I would expect to get the following as the output instead: Sum[Log[f[i]], {i,1,n}]

Is it possible to tweak the code somehow to achieve such behavior?

  • 1
    $\begingroup$ I think you only can introduce a rule like this: rule = Log[Product[f_[i], {i, 1, n_}]] :> Sum[Log[f[i]], {i, 1, n}] and apply it to such expressions. $\endgroup$ – Alexei Boulbitch Apr 1 '19 at 12:35

Amplifying @AlexeiBoulbitch 's comment: you may have to implement this transformation manually, as it makes a lot of assumptions.

A = Log[Product[f[i], {i, 1, n}]]

$$ \log \left(\prod_{i=1}^n f(i)\right) $$

A /. Log[Product[a_, b_]] :> Sum[Log[a], b]

$$ \sum_{i=1}^n \log(f(i)) $$

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