为什么log（xy）= log（x）+ log（y）在SymPy中不起作用？

Question

Why does log( xy ) = log( x ) + log( y ) not work in SymPy?

I tried this:

from sympy import *
var('x y')
print(simplify(log(x*y)))
print(expand(log(x*y)))
print(collect(log(x*y),x))
print(solve(log(x*y),x))
# log(x*y)
# log(x*y)
# log(x*y)
# [1/y]

Answer 1

log( xy ) = log( x )+log( y ) does not always hold. More specifically, this may to problems if both x and y are negative or in the complex domain. The Wolfram Alpha link you gave also states “Alternate form assuming x and y are positive”.

To see this relation in SymPy, you have to mark the symbols x and y as positive, eg like this:

from sympy import symbols,log
x,y = symbols("x,y",positive=True)
expr = log(x*y)
expr.expand()

Alternatively (as hinted at by user6655984 ) you can use the force hint to let SymPy assume that everything is maximally benign:

from sympy import log
from sympy.abc import x,y
expr = log(x*y)
expr.expand(force=True)