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combine/ln

combine logarithmic terms

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

combine(f, ln)

combine(f, ln, t)

combine(f, ln, t, m)

Parameters

f

-

any expression

t

-

type

m

-

the name 'symbolic'

Description

• 

In the case combine(f, ln), expressions involving sums of logarithms are combined by applying the following transformations:

alnxlnxaprovidedaargumentx=argumentxa

lnx+lnylnxyprovidedargumentxy=argumentx+argumenty

  

where the coefficient a must be a rational constant and the argument of x and y must be in the region where this transformation is valid, unless 'symbolic' is specified.

• 

In the case combine(f, ln, t), the first transformation is done if the coefficient a is of type t. Often it is useful to restrict the transformation to be done only if a is an integer instead of a rational. Also, by specifying the type anything, the transformation is done in all valid cases, provided of course that the coefficient a itself is not a logarithm.

Examples

combine3ln22ln3,ln

6ln13232/3

(1)

combinealnx+3lnxln1x+ln1+x2,ln

alnx+3lnxln1x+ln1+x

(2)

assumea&comma;real&semi;assume0<x

combinealnx&plus;3lnxln1x&plus;ln1&plus;x2&comma;ln

a~lnx~ln1x~&plus;lnx~31&plus;x~

(3)

combinealnx&plus;3lnxln1x&plus;ln1&plus;x2&comma;ln&comma;integer

ln1&plus;x~x~3&plus;a~lnx~&plus;12ln1&plus;x~

(4)

combinealnx&plus;3lnxln1x&plus;ln1&plus;x2&comma;ln&comma;anything

ln1x~&plus;lnx~a~x~31&plus;x~

(5)

additionallyx&comma;RealRange0&comma;1

combinealnx&plus;3lnxln1x&plus;ln1&plus;x2&comma;ln&comma;anything

lnx~a~x~31&plus;x~1x~

(6)

combineblny&plus;3lnyln1y&plus;ln1&plus;y2&comma;ln&comma;anything&comma;symbolic

lnyby31&plus;y1y

(7)

See Also

additionally

assume

combine

ln

 


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