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Log rules are working for actual values, but fail for symbolic ones. What am I doing wrong?

var('a b')
c = bool(log(a*b) == log(a) + log(b));print(c)
c = bool(log(5*3) == log(5) + log(3));print(c)
c = log(5*3).n(); print(c)
c = log(5).n() + log(3).n(); print(c)

False False 2.70805020110221 2.70805020110221

Log rules are working for actual values, but fail for symbolic ones. What am I doing wrong?

var('a b')
c = bool(log(a*b) == log(a) + log(b));print(c)
c = bool(log(5*3) == log(5) + log(3));print(c)
c = log(5*3).n(); print(c)
c = log(5).n() + log(3).n(); print(c)

False
False
2.70805020110221
2.70805020110221