Sage says equation isn't true while Mathematica says it is

edit

Note that Sage only says True if it can prove it is true, otherwise returning False.

Yes, you know it, but sage needs some help:

We really need a subpage to refer for this kind of bool-evaluation of symbolic equalities, it will be the hit.

So let us provide the help!

sage: var( 'mu,sigma' )
(mu, sigma)
sage: var( 'mu,sigma' );
sage: assume(sigma > 0)
sage: assume(mu > 0)
sage: eq = mu + 0.5*log(2*pi*sigma^2*e) == log(sqrt(2)*sqrt(pi)*sigma*e^(mu + 0.5))
sage: bool(eq)
False
sage: bool(eq.canonicalize_radical())
True
sage: eq.canonicalize_radical()
1.0*mu + 0.5*log(2) + 0.5*log(pi) + 1.0*log(sigma) + 0.5 == 1.0*mu + 0.5*log(2) + 0.5*log(pi) + 1.0*log(sigma) + 0.5

EDIT: Sorry, i'm afraid i was editing a comment of muxamilian...

@dan_fulea - do you have a Trac account? Then you could put something to add this to the doc.