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Mathematics Algebra Wolfram Language

Combine sum of logarithms to logarithm of a product?

Ralph Trenkler

Ralph Trenkler, Universität Hamburg

Posted 5 years ago

Is there any Mathematica command with which I can combine a sum of logarithms into a logarithm of a product? Log[a]+Log[b] -> Log[a*b], Log[a]-Log[b] -> Log[a/b], etc.

POSTED BY: Ralph Trenkler

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Kyle Martin

Kyle Martin, WOLFRAM

Posted 5 years ago

Perhaps In[6]:= FullSimplify[Log[a] + Log[b], a > 0 && b > 0] Out[6]= Log[a b] In[7]:= FullSimplify[Log[a] - Log[b], a > 0 && b > 0] Out[7]= Log[a/b] is what you're after.

POSTED BY: Kyle Martin

Dublin Nichols

Posted 5 years ago

Any idea why these logs are not combined? In[26]:= FullSimplify[ Log[T0^2/(Ti1 Ti2)] - Log[((Ti1 + ((c dT)/2 - c (-T0 + Ti1))/ c) (Ti2 + (-((c dT)/2) - c (-T0 + Ti2))/c))/(Ti1 Ti2)]] Out[26]= Log[T0^2/(Ti1 Ti2)] - Log[-((dT^2 - 4 T0^2)/(4 Ti1 Ti2))] EDIT: Mathematica needs to know that these variables are not 0. Adding this line fixes it. $Assumptions = {T0 > 0, Ti1 > 0, Ti2 > 0, c > 0}

Any idea why these logs are not combined?

In[26]:= FullSimplify[
 Log[T0^2/(Ti1 Ti2)] - 
  Log[((Ti1 + ((c dT)/2 - c (-T0 + Ti1))/
      c) (Ti2 + (-((c dT)/2) - c (-T0 + Ti2))/c))/(Ti1 Ti2)]]

Out[26]= Log[T0^2/(Ti1 Ti2)] - Log[-((dT^2 - 4 T0^2)/(4 Ti1 Ti2))]

EDIT: Mathematica needs to know that these variables are not 0. Adding this line fixes it.

$Assumptions = {T0 > 0, Ti1 > 0, Ti2 > 0, c > 0}

POSTED BY: Dublin Nichols

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