Use the Logarithm field of the Options > Mode Settings > Simplification command19_L5FP to control the collection or expansion of expressions involving logarithms.  The transformation

LN(x) + LN(z)  ⇐⇒  LN(x·z)

is valid if z is real or complex and x is nonnegative.  The transformation

                  k  
k·LN(x)  ⇐⇒  LN(x ) 

is valid if k is a rational number, and x is nonnegative or k lies in the interval (-1, 1].  The Logarithm field provides the following options:

•        Select the Collect option to apply both transformations to the right when simplifying expressions.

•        Select the Expand option to apply both transformations to the left when simplifying expressions.

•        Select the Auto option to apply the transformations in such a way as to produce the most compact and attractive form having the fewest number of radicals when simplifying expressions.  Auto is the factory default logarithm mode setting.


For example, if the Collect option is selected, the expression

LN(x·y^4 + 2·x·y^2 + x)/2

simplifies to

        2       
LN(√x·(y  + 1)) 

whereas if the Expand option is selected, it simplifies to

 LN(x)        2      
——————— + LN(y  + 1) 
   2                 

whereas if the Auto option is selected, it simplifies to

        2     2   
 LN(x·(y  + 1) )  
————————————————— 
        2         


When a new logarithm transform direction is selected, this command generates an expression of the form

Logarithm := direction

where direction is Auto, Collect, or Expand.  The logarithm transform direction can also be changed by entering an expression of the above form using upper and lower case exactly as shown on the expression entry line.


Other Options > Mode Settings > Simplification command19_L5FP fields

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