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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)

logbx

Parameters

x

-

expression

b

-

base

Description

• 

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

• 

For complex-valued expressions x, lnx=lnx+Iargx, 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 logbx=y<==>x=by.  log is extended to general complex b and x by logbx=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=log10x.

• 

lnx=log&ExponentialE;x.

Examples

ln1

0

(1)

&DifferentialD;&DifferentialD;xlnx

1x

(2)

ln3.14&plus;2.71I

1.422562238+0.7120258406I

(3)

ln3&plus;4I

ln3+4I

(4)

evalc

ln5+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&ExponentialE;x

lnx

(10)

logbx

lnxlnb

(11)

log1065

ln65ln10

(12)

log10100

2

(13)

log2&ExponentialE;

1ln2

(14)

evalf

1.442695041

(15)

log55xlog5x

ln5xln5lnxln5

(16)

simplify

1

(17)

solvelog62y&equals;2&comma;y

18

(18)

convertarcsinx&comma;ln

−IlnIx+x2+1

(19)

See Also

argument

convert

evalc

evalf

ilog10

initialfunctions

RealDomain

simplify

solve