Rewrite log in exponents

B r u n o
1603 ●5 ●21 ●43

Does there exist a method in Sage's symbolic ring that would be able to (automatically) rewrite expressions such as $3^{\log n}$ into $n^{\log 3}$?

Here I assume that $n$ is a positive integer.

Remark: I am quite surprised (and therefore pessimistic for my question) by the following:

sage: [bool(3^(log(i)) == i^(log(3))) for i in range(1, 12)]
[True, True, True, True, False, False, True, False, True, False, False]

Comments

I do not know if this would be helpful for your question but .canonicalize_radical() solves the problem in your example:

var('k')
[bool((3^(log(k)) - k^(log(3))).canonicalize_radical()==0) for k in range(1, 12)]

I used the variable k instead of i which is sqrt(-1).

tolga ( 2021-06-09 19:08:50 +0100 )edit

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