# How to calculate logarithms and inverse logarithms in Excel?

In this lesson, I will remind you what a logarithm is. 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 with the theory.

## What is a logarithm?

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

Loga b=c ac=b

For example

Log2 3 = 8 because 23=8

## What is a common logarithm?

A common logarithm is just a logarithm with a base of 10. You don't need to write 10 as a base. Log10 x = log x

For example:

log 1 = 0

log 10 = 1

log 1000 = 3

## What is a natural logarithm?

A natural logarithm is a special kind of logarithm. A natural logarithm is a logarithm to the base e. e is a mathematical constant which is approximately equal to 2.718281828459. Instead of loge 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. Use the EXP function to find the inverse natural log.

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

To calculate the logarithm in Excel, just use the 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 the inverse of a logarithm, use a 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 a common logarithm and inverse of common logarithm?

To calculate the logarithm in Excel, just use the LOG function.

=LOG10(n)

n = number

The base of a 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 the inverse of a common logarithm, use a 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 a natural logarithm and inverse of natural logarithm?

To calculate the natural logarithm in Excel, just use the LN function.

=LN(n)

n = number

The base of a 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 the inverse of a natural logarithm, use the 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

## How to get rid of ln?

To get rid of LN in Excel, you can use the EXP function, which is the inverse of the natural logarithm function.

Here's an example:

Let's say you have a cell with the formula "=LN(10)" and you want to get rid of the "LN" function.

1. Click on the cell containing the formula.
2. Type "=" to start a new formula.
3. Type "EXP(" to start the "exp" function.
4. Highlight the cell containing the "LN" function (in this case, it's the cell with the formula "=LN(10)").
5. Type ")" to close the "exp" function.

Your new formula should look like this: "=EXP(A1)" (assuming the cell containing the "LN" function is A1).

Press enter and the formula will calculate the result of the "exp" function, which is the inverse of the natural logarithm function. In this example, the result would be "22026.47", which is the value of e^ln(10).

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