The LN function will calculate the natural logarithm of any given number.

## Contents:

## Syntax

`= LN(`*number*)

*number -* a positive number you wish to return the natural logarithm of

### Explanation

The LN function is part of the "Math and Trigonometry" group of functions within Excel.

The LN function in Excel calculates the natural logarithm of a given positive number. The natural logarithm is the logarithm to the base "e" (approximately 2.71828). When you use the LN function, Excel computes the power to which "e" must be raised to obtain the input number.

When you enter the LN function with a specific number, Excel uses a numerical algorithm to calculate the natural logarithm. These algorithms, such as the Taylor series or Newton's method, provide an approximation of the natural logarithm, as it is not possible to compute the exact value for most numbers.

*Note:*

If the input number is negative a #NUM! error will be returned

### Examples

## How to Calculate How the Time for Growth Rates to Double in Size

In this example, we'll demonstrate how to calculate how long it takes a population to double in size.

We'll take a look at population growth, but this same concept can be applied to investments, inflation, consumption of goods, or any set of data that undergoes change over time.

In the table below, we have a list of countries and their respective population growth rates, and we want to calculate how long it will take their population to double if growth rates remain static.

We can use the following formula to calculate how long it will take each country's population to double:

`= LN(2) / LN(1 + growth_rate)`

For a more in depth look at the math behind this equation, __this link__ has a great breakdown. But basically, we start with a standard exponential growth equation:

`future_value = initial_value * e^(growth_rate * time)`

And if we want to calculate the time to double the future value, we need to time both sides by 2, and then take the natural log of each side. Leaving us with the formula seen above of:

`double_time = LN(2) / growth_rate`