Python Power and Logarithm Functions

cbrt() Function

The cbrt() function in the math module returns the cube root of a number.

Syntax

math.cbrt(x)

Parameters

• x − Numeric operand

Return Value

The cbrt() function returns the cube root of a given number.

Example

from math import cbrt

x = 27
cbr = cbrt(x)
print ("x: ",x, "cbrt(x): ", cbr)

x = 100
cbr = cbrt(x)
print ("x: ",x, "cbrt(x): ", cbr)

x = 8.8
cbr = cbrt(x)
print ("x: ",x, "cbrt(x): ", cbr)

This will produce the following output −

x: 27 cbrt(x): 3.0
x: 100 cbrt(x): 4.641588833612779
x: 8.8 cbrt(x): 2.0645602309127344

exp() Function

The exp() function returns the exponential value of x: ex.

Syntax

The syntax of the exp() function is as follows:

import math
math.exp(x)

Note − This function cannot be accessed directly. Therefore, we need to import the math module and then call it using the math static object.

Parameters

• x − This is a numeric expression.

Return Value

This method returns the exponential of x: ex.

Example

The following example shows how to use the exp() method.

import math # This will import the math module
print ("math.exp(-45.17) : ", math.exp(-45.17))
print ("math.exp(100.12) : ", math.exp(100.12))
print ("math.exp(100.72) : ", math.exp(100.72))
print ("math.exp(math.pi) : ", math.exp(math.pi))

When you run the above program, the following output is produced.

math.exp(-45.17) : 2.4150062132629406e-20
math.exp(100.12) : 3.0308436140742566e+43
math.exp(100.72) : 5.522557130248187e+43
math.exp(math.pi) : 23.140692632779267

exp2() Function

The exp2() function in the math module returns 2 raised to the power of x. It is equivalent to 2**x.

Syntax

math.exp2(x)

Parameters

• x – Numeric operand

Return Value

This function returns x raised to the power of 2.

Example

from math import exp2

x = 6
val = exp2(x)
print ("x: ",x, "exp2(x): ", val)
print ("cross-check:", 2**6)
x = -3
val = exp2(x)
print ("x: ",x, "exp2(x): ", val)

x = 2.5
val = exp2(x)
print ("x: ",x, "exp2(x): ", val)

It will produce the following output –

x: 6 exp2(x): 64.0
cross-check: 64
x: -3 exp2(x): 0.125
x: 2.5 exp2(x): 5.656854249492381

expm1() Function

The expm1() function of the math module computes and returns e raised to the power of x minus 1. Here, e is the base of the natural logarithm. The expm1() function provides a full-precision method for computing this quantity.

Syntax

math.expm1(x)

Parameters

• x – An operand of type int or float.

Return Value

This function returns the exponential value of a number – 1.

Example

from math import expm1

x = 6
val = expm1(x)
print ("x: ",x, "expm1(x): ", val)

x = -3
val = expm1(x)
print ("x: ",x, "expm1(x): ", val)

x = 2.5
val = expm1(x)
print ("x: ",x, "expm1(x): ", val)

This will produce the following output −

x: 6 expm1(x): 402.4287934927351
x: -3 expm1(x): -0.950212931632136
x: 2.5 expm1(x): 11.182493960703473

log() Function

The log() function returns the natural logarithm of x, where x > 0.

Syntax

The following is the syntax of the log() function −

import math
math.log( x )

Description – This function is not accessible directly, so we need to import the math module and then call it through the math static object.

Parameters

• x – This is a numeric expression.

Return Value

This function returns the natural logarithm of x when it is greater than 0.

Example

The following example demonstrates the use of the log() method:

import math # This will import the math module
print ("math.log(100.12) : ", math.log(100.12))
print ("math.log(100.72) : ", math.log(100.72))
print ("math.log(math.pi) : ", math.log(math.pi))

When we run the above program, it produces the following output:

math.log(100.12) : 4.6063694665635735
math.log(100.72) : 4.612344389736092
math.log(math.pi) : 1.1447298858494002

log10() Function

The log10() function returns the base 10 logarithm of x (for x > 0).

Syntax

The syntax of the log10() function is as follows:

import math
math.log10(x)

Note − This function cannot be used directly. We need to import the math module and then use the math static object to call this function.

Parameters

• x − This is a numeric expression.

Return Value

This function returns the base-10 logarithm of x, where x > 0.

Example

The following example shows the use of the log10() function.

import math # This will import the math module
print ("math.log10(100.12) : ", math.log10(100.12))
print ("math.log10(100.72) : ", math.log10(100.72))
print ("math.log10(119) : ", math.log10(119))
print ("math.log10(math.pi) : ", math.log10(math.pi))

When we run the above program, it will produce the following output –

math.log10(100.12) : 2.0005208409361854
math.log10(100.72) : 2.003115717099806
math.log10(119) : 2.0755469613925306
math.log10(math.pi) : 0.49714987269413385

log1p() Function

The log1p() function in the math module returns the natural logarithm (base e) of 1+x. The result is exact when x is close to zero.

Syntax

math.log1p(x)

Parameters

• x – int or float operand.

Return Value

This function returns the natural logarithm of 1+x.

Example

from math import log1p

x = 4
val = log1p(x)
print ("x: ",x, "log1p(x): ", val)

x = 2.5
val = log1p(x)
print ("x: ",x, "log1p(x): ", val)

x = -3
val = log1p(x)
print ("x: ",x, "log1p(x): ", val)

This will produce the following output –

x: 4 log1p(x): 1.6094379124341003
x: 2.5 log1p(x): 1.252762968495368
Traceback (most recent call last):
File "C:Usersmlathexamplesmain.py", line 12, in <module>
val = log1p(x)
^^^^^^^^
ValueError: math domain error

Negative exception: A ValueError exception is raised when x is negative.

log2() Function

The log2() function in the math module returns the base-2 logarithm of x. This is usually more accurate than log(x, 2).

Syntax

math.log2(x)

Parameters

• x – integer or floating-point operand

Return Value

This function returns the base-2 logarithm of x.

Example

from math import log2

x = 4
val = log2(x)
print ("x: ",x, "log2(x): ", val)

x = 2.5
val = log2(x)
print ("x: ",x, "log2(x): ", val)

x = -3
val = log2(x)
print ("x: ",x, "log2(x): ", val)

This will produce the following output: −

x: 4 log2(x): 2.0
x: 2.5 log2(x): 1.3219280948873624
Traceback (most recent call last):
File "C:Usersmlathexamplesmain.py", line 12, in <module>
val = log2(x)
^^^^^^^
ValueError: math domain error

pow() Function

The pow() function returns x raised to the power of y. math.pow() converts its two arguments to floating-point numbers. Use ** or the built-in pow() function to calculate exact integer powers.

Syntax

The syntax of the pow() function is as follows:

import math
math.pow( x,y )

Note – This function cannot be accessed directly, so we need to import the math module and then call it using the math static object.

Parameters

• x, y – This is a numeric expression.

Return Value

This function returns x raised to the power of y.

Example

The following example demonstrates the use of the pow() function –

import math # This will import the math module
print ("math.pow(100, 2) : ", math.pow(100, 2))
print ("math.pow(100, -2) : ", math.pow(100, -2))
print ("math.pow(2, 4) : ", math.pow(2, 4))
print ("math.pow(3, 0) : ", math.pow(3, 0))

The following output will be generated −

math.pow(100, 2) : 10000.0
math.pow(100, -2) : 0.0001
math.pow(2, 4) : 16.0
math.pow(3, 0) : 1.0

sqrt() Function

The sqrt() function returns the square root of a number, x, where x > 0.

Syntax

The syntax of the sqrt() function is as follows:

import math
math.sqrt( x )

Note − This function cannot be accessed directly, so we need to import the math module and then call it using the math static object.

Parameters

• x − This is a numeric expression.

Return Value

This method returns the square root of x when x > 0.

Example

The following example shows the usage of the sqrt() function −

import math # This will import math module
print ("math.sqrt(100) : ", math.sqrt(100))
print ("math.sqrt(7) : ", math.sqrt(7))
print ("math.sqrt(math.pi) : ", math.sqrt(math.pi))

When we run the above program, it will produce the following output –

math.sqrt(100) : 10.0
math.sqrt(7) : 2.6457513110645907
math.sqrt(math.pi) : 1.7724538509055159