MATLAB: How to check validity of logarithm rule

logarithmsMATLAB

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

Best Answer

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
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