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ln

The Natural Logarithm

log

The General Logarithm

log10

The Common Logarithm

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

ln(x)

 

log(x)

 

log10(x)

 

log[b](x)

log[b]x

Parameters

x

-

expression

b

-

base

Description

• 

The natural logarithm, ln, is the logarithm with base &ExponentialE;&equals;2.71828...  For 0<x we have lnx&equals;y <==> x&equals;&ExponentialE;y.

• 

For complex-valued expressions x, lnx&equals;lnx&plus;Iargumentx, where π<argument(x)<=π.  Throughout Maple, this computation is taken to be the definition of the principal branch of the logarithm.

• 

The log function is the general logarithm.  For 0<x and 0<b we have log&lsqb;b&rsqb;x&equals;y<==>x&equals;by.  log is extended to general complex b and x by log&lsqb;b&rsqb;x&equals;lnxlnb.

• 

The default value of the base b is &ExponentialE;.

• 

You can enter  the function log with base b using either the 1-D or 2-D calling sequence.  Similarly, e can also be entered as exp(1) in 1-D.  See exp for more about the exponential function.

• 

log10x&equals;log&lsqb;10&rsqb;x.

• 

lnx&equals;log&lsqb;&ExponentialE;&rsqb;x.

Examples

ln1

0

(1)

&DifferentialD;&DifferentialD;xlnx

1x

(2)

ln3.14&plus;2.71I

1.422562238&plus;0.7120258406I

(3)

ln3&plus;4I

ln3&plus;4I

(4)

evalc

ln5&plus;Iarctan43

(5)

ln10000

4ln10

(6)

The default value of the base b is &ExponentialE;.

log10000

4ln10

(7)

log&ExponentialE;3

3

(8)

log1010000

4

(9)

log&lsqb;&ExponentialE;&rsqb;x

lnx

(10)

log&lsqb;b&rsqb;x

lnxlnb

(11)

log1065

ln65ln10

(12)

log&lsqb;10&rsqb;100

2

(13)

log&lsqb;2&rsqb;&ExponentialE;

1ln2

(14)

evalf

1.442695041

(15)

log&lsqb;5&rsqb;5xlog&lsqb;5&rsqb;x

ln5xln5lnxln5

(16)

simplify

1

(17)

solvelog&lsqb;6&rsqb;2y&equals;2&comma;y

18

(18)

convertarcsinx&comma;ln

IlnIx&plus;x2&plus;1

(19)

See Also

argument

convert

evalc

evalf

ilog10

initialfunctions

RealDomain

simplify

solve

 


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