In this lesson I remind you what is logarithm. You will also get to know how to calculate logarithm, common logarithm, natural logarithm, inverse logarithm and inverse natural logarithm in Excel.

Let's start from the theory.

## What is logarithm?

The easiest way to understand what logarithms are is to understand this mathematical formula:

**Log _{a} b=c a^{c}=b**

For example

Log_{2} 3 = 8 because 2^{3}=8

## What is common logarithm?

Common logarithm is just logarithm with base 10. You don't need to write 10 as a base Log_{10} x = log x

For example:

log 1 = 0

log 10 = 1

log 1000 = 3

## What is natural logarithm?

Natural logarithm is a special kind of a logarithm. Natural logarithm is a logarithm to the base e. e is mathematical constant which is is approximately equal to 2.718281828459. Instead of log_{e} x we use ln x

Microsoft Excel has built-in functions to calculate the logarithm of a number with a specified base, the logarithm with base 10, and the natural logarithm. To calculate the inverse log of a number in the first two cases, raise the base to the power of the value returned by the particular logarithm function being used. To find the inverse natural log, use the EXP function.

## How to calculate logarithm and inverse of logarithm?

To calculate logarithm in Excel just use LOG function.

**=LOG(n,b) **

n = number

b = base

=LOG(16,4) – result is 2

=LOG(81,9) – result is 2

=LOG(125,5) = result is 3

=LOG(512,2) – result is 9

To calculate an inverse of logarithm use power function

**=POWER(base, result)** – watch out not to change the sequence!

=POWER(4, 2) – equals 16

=POWER(9, 2) – equals 81

=POWER(5, 3) – equals 125

=POWER(2, 9) – equals 512

## How to calculate common logarithm and inverse of common logarithm?

To calculate logarithm in Excel just use LOG function.

**=LOG10(n) **

n = number

Base of common logarithm is always 10.

=LOG10(100) – result is 2

=LOG10(1) – result is 0

=LOG10(1000) = result is 3

=LOG10(0.0000001) – result is -7

To calculate an inverse of common logarithm use power function

**=POWER(10, result)** – always 10 because this is the base of common logarithm

=POWER(10, 2) – equals 100

=POWER(10, 0) – equals 1

=POWER(10, 3) – equals 10

=POWER(10, -7) – equals 0.0000001

## How to calculate natural logarithm and inverse of natural logarithm?

To calculate natural logarithm in Excel just use LN function.

**=LN(n) **

n = number

Base of natural logarithm is always e

=LN(1) – result is 0

=LN(2.718281828) – result is 1

=LN(10) = result is 2.30258509

=LN(100) – result is 4.60517019

To calculate an inverse of natural logarithm use EXP function

**=EXP(n)**

n = number

=EXP(0) – equals 1

=EXP(1) – equals 2.718281828

=EXP(2.30258509) – equals 10

=EXP(4.60517019) – equals 100