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simplify/ln

simplify expressions involving logarithms

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

simplify(expr, ln)

Parameters

expr

-

any expression

ln

-

literal name; ln

Description

• 

The simplify/ln function is used to simplify logarithmic expressions. It applies the following simplifications whenever it can determine that the appropriate conditions hold:

 

 

Simplification

Provided

 

 

lnab ==> blna

signuma=1 and b is real

lnab ==> blna

signuma=1 and b is even

lnab ==> blna

signuma=1 and b is odd

lnab ==> 12blna2

a is real and b is even

lnab ==> blna

a is real and b is odd

 

 

lnxy ==> lnx+lny

0<x and signumy is unknown

lnxy ==> lnx&plus;lny

signumx&equals;1

lnxy ==> lnx+lny+Iπ

signumx&equals;1 and signumy&equals;1

 

 

ln&ExponentialE;x ==> x

x is real

lnLambertWx ==> lnxLambertWx

x is real

 

 

• 

In the case of an integer argument to ln, the integer is factored and the logarithm is returned as a sum of logarithms.

• 

In the case of a sum of terms as the argument to ln, the integer content of the sum is factored out and the logarithm is returned as a sum of two logarithms.

• 

Making the appropriate assumptions on the names in the expression to be simplified (see assume) provides simplify with enough information to apply the above identities correctly.

Examples

It is inappropriate to apply the above identities in these cases since nothing is known about n, x, and y:

simplifylnx3&comma;ln

lnx3

(1)

simplifylnxy

lnxy

(2)

simplifyln&ExponentialE;x&comma;ln

ln&ExponentialE;x

(3)

simplifylnyn&comma;ln

lnyn

(4)

However, by making appropriate assumptions on the variables, enough information is provided to correctly apply the identities:

assumen&comma;even

assumex&comma;real

assumey<0

simplifylnx3&comma;ln

lnx~3

(5)

simplifylnxy

lny~&plus;lnx~

(6)

simplifyln&ExponentialE;x

x~

(7)

simplifylny3&comma;ln

3lny~&plus;I&pi;

(8)

simplifylnyn&comma;ln

n~lny~

(9)

Simplifications involving integer factors:

simplifyln40a&plus;15b&comma;ln

ln5&plus;ln8a&plus;3b

(10)

simplifyln345366&comma;ln

ln2&plus;2ln3&plus;ln7&plus;ln2741

(11)

See Also

assume

combine

simplify

 


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