Purpose

Return value

Syntax

=LN(number)
  • number - A number to take the natural logarithm of.

Using the LN function

The LN function returns the natural logarithm of a given number. The natural logarithm is equivalent to log base e of a number, where e is Euler’s number , a mathematical constant with the approximate value 2.71828182845904. The LN function is the inverse of the EXP function and is used to model exponential decay.

The LN function takes just one argument, number , which should be a positive number.

Examples

=LN(1) // returns 0
=LN(e) // returns 1
=LN(e^2) // returns 2

The equivalent form of the natural logarithm function is given by:

=LN(number)=LOG(number,e) // Where e ≈ 2.7128 or EXP(1)

Graphs

Below is a graph of the natural log logarithm:

Graph of the natural logarithm function. - 1

The natural logarithm function and exponential function are the inverse of each other, as you can see in the graph below:

Graph of the natural logarithm and exponential function. - 2

This inverse relationship can be represented with the formulas below, where the input to the LN function is the output of the EXP function :

= LN(EXP(1)) // returns 1
= LN(EXP(2)) // returns 2
= LN(EXP(n)) // returns n

See wumbo.net for a more detailed explanation of key math concepts and formulas.

Notes

  • The natural logarithm function can be defined as the area under a hyperbola.
  • The function is used in applications relating to compound interest.

Purpose

Return value

Syntax

=LOG(number,[base])
  • number - Number for which you want the logarithm.
  • base - [optional] Base of the logarithm. Defaults to 10.

Using the LOG function

The LOG function returns the logarithm of a given number, using the provided base.

The LOG function takes two arguments , number and base . The value provided for number should be a positive real number. The base argument represents the base of the logarithm. Base is optional and defaults to 10 if not provided.

Examples

The logarithm of 16 with base 2 (the power to which 2 must be raised to equal 16) is 4:

=LOG(16, 2) // returns 4

The logarithm of 100 with base 10 (the power to which 10 must be raised to equal 100) is 2:

=LOG(100,10) // returns 2

Because the base argument defaults to 10, the formulas below are equivalent:

=LOG(100,10) // returns 2
=LOG(100) // returns 2

The LOG10 function also returns the base 10 logarithm of a number:

=LOG10(100) // returns 2
=LOG10(1000) // returns 3

Notes

  • If number or base are not numeric, LOG returns #VALUE!
  • The LOG10 function also returns the base 10 logarithm of a number.