How do I check validity of logarithm rule?

Hello, I want to check if the logarthm product rule is true using MATLAB R2018a.

I have tested the functions logical and isAlways without success. My code:

syms a;
syms b;

isAlways (log(a*b) == log(a)+log(b))

Which returns the following in command window:

Warning: Unable to prove 'log(a*b) == log(a) + log(b)'. 
> In symengine
  In sym/isAlways (line 42)
  In test (line 12) 

ans =

  logical

   0

Answer 1

[Stephan]

Hi,

Matlab can prove if you give an assumption additionally:

syms a b;
assume([a b],'positive');
assumptions
result = isAlways(log(a*b) == log(a)+log(b))

results in:

ans =
 
[ 0 < a, 0 < b]
 

result =

  logical

   1   

Best regards

Stephan