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## #40 log(27)/log(3) does not simplify to 3

open
nobody
None
4
2007-05-01
2007-04-29
Anonymous
No

log(27)/log(3), and similar expressions, do not simplify (in this case to 3).

I used version 5.9.3 - if it's corrected in later versions, sorry for the post :)

## Discussion

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This is not a bug; it is a feature request.

That is, Maxima does not perform all possible simplifications by default. You are asking that it handle an additional case. This has in fact been discussed.

There are many cases which the default simplifier does not simplify, and where you need to call a special simplifier:

ex: sin(x)^2+cos(x)^2;
trigsimp(ex) or trigrat(ex) or ratsimp(trigsimp(ex)) => 1

ex: (x^2-1)/(x-1);
ratsimp(ex) or rat(ex) or factor(ex) => x+1

ex: (x-y)/(sqrt(x)-sqrt(y));

ex: (2*sqrt(2)-2)/sqrt(2);
ratsimp(ex),algebraic => 2-sqrt(2)
(there is actually a bug hidden inside this one...)

ex: log(27)/log(3);

Radcan is perhaps overkill, but that's the current tool to do this:

ex: log(72)/log(2);

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set numer:true

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Anon comment
set numer:true
works OK in this particular case -- it gives exactly 3.0. But Maxima is a symbolic system, and our goal is to give the exact result (even if it is not a round number) in all cases.

Consider, for example, cases like log(72)/log(2), where the exact symblic answer (given by radcan) is (2*log(3)+3*log(2))/log(2) == 2*log(3)/log(2)+3. Numer doesn't help with that.