LN in Google Sheets

What Is LN Function in Google Sheets?

The LN function in Google Sheets is used to calculate the natural logarithm of any number. The LN function is used to calculate the natural logarithm which is to the base e of a number. This function is particularly helpful in various fields such as physics, engineering, and statistics where we may be required to find the rate of growth and in compound interest calculations.

The opposite of exponentials is logarithms. Using exponents, we can find how many times to multiply a number by itself. Whereas in the case of logarithms, you can find what power is needed to raise a base number to get another number. In natural logarithms, the base is e. For example, in the sheet below, we want to find the natural logarithm of 10. Enter the following formula in cell B1.

=LN(10)

It returns the natural logarithm of 10, which is approximately 2.303.

The LN in Google Sheets calculates the natural logarithm of a given number. This means the logarithm to the base e, which is approximately equal to 2.718.
The syntax is as follows: =LN(value). Here, the value should be a positive number greater than zero.
If the value parameter is zero or negative, the function will return an #NUM! Error.
The LN function is beneficial when used in scientific, engineering, and financial applications, especially for calculations involving exponential growth or decay.
You can apply the LN function to a range of cells.

Syntax

Before we proceed with the article in detail, let us find the syntax of LN in Google Sheets. It is as follows:

=LN(value)

Value (should be greater than zero): Here, the value is a positive number for which you must calculate the natural logarithm.

How to Use LN Function in Google Sheets?

Now, that we know the syntax, let’s find out how to put the LN function to use! There are two ways to do it: manually or through the Google menu bar. The steps are as shown below.

Entering NORM.INV in Google Sheets Manually

Step 1: We have a set of numbers as shown in the sheet below. First, click on the cell where you want the result of the first natural logarithm. Here, it is B1.

Step 2: Type =LN( into the cell.

Step 3: Type in the cell reference that contains the value you want to calculate the natural logarithm for. Here, we calculate the natural logarithm of the number in cell A1.

Step 4: Close the bracket and press Enter. There you are! You get the natural logarithm of the value in A1. Drag the formula till cell B5.

You notice that you get the LN value in Google Sheets for all positive numbers. If it’s zero or negative, you’ll see a #NUM! Error because logarithms of these numbers don’t exist.

Using the Google Menu Bar

First, go to the cell where you wish to enter the LN formula.
In the Google menu bar, click on “Insert” ➝ “Function” ➝ “Math” ➝ “LN.“
Enter the required arguments. Close the bracket and press the “Enter” key.

Examples

The LN Google Sheets formula is used to calculate the natural logarithm of a number. It is used in scenarios such as calculating exponential growth or decay or calculation of the compound interest. It is also helpful to find the probability of an event occurring. Let us look at the interesting examples below.

Example #1 – Basic Logarithmic Calculation

In this simple example, let us use the LN function is useful to easily calculate the half-life in radioactive decay where a substance decays over time. The general formula for half-life is as follows:

Using the LN function in Google Sheets, this equation can be written as follows to find the half-life:

t=ln(2)/λ

We have an initial amount of 500 units of a radioactive substance. It has a decay constant of 0.06. Let us enter these details to calculate the half-life.

Step 1: Enter these details in a Google Sheet as shown below:

Step 2: Calculate The time for Half-Life using the following formula in cell B3:

=B1*LN(2) / B2. Press Enter.

This function will return the time it takes for the given quantity of substance to decay to half of its original amount.

Example #2 – Compound Interest Formula

In the field of finance, natural logarithms can be particularly handy when we calculate continuous growth, especially in calculations involving compound interest. Let us look at an interesting example.

The formula to find the compound interest is as follows:

A = P e^rt.

Where:

A is the amount of money accumulated after t years, including interest and P is the principal amount (the initial investment). Also, r is the rate of interest per period and t is the time of the investment.

Using LN in Google Sheets, we can calculate the time taken to double the investment. Here the investment amount is $5,000 and we need the final amount as $10,000. The rate of interest is 0.05.

Step 1: Enter all the details as shown below.

Step 2: You can use the following formula to compute the time taken to double the investment.

t = ln(A/P)/r

Apply it to cell B4 as follows:

=LN(B3/B1)/B2. Press Enter.

Result: The formula will return the time in years it takes for the principal to grow from $5,000 to $10,000 at a 5% annual interest rate.

Example #3 – Calculating Growth Rates Over Time

Let’s say you’re analyzing the population of a town and tracking its growth over time. You have a column with the yearly population and wish to analyze the growth rate. Using the LN function can help you interpret the population growth.

For instance, if the population in 2020 is 1,200, in 2021 it is 1,700, in 2022 it is 2,400, and in 2023 it is 2,900, you can apply the LN function to each of these values to get a logarithmic scale of growth.

Step 1: The formula to calculate the population growth per year would be as follows:

g = ln(Y_t/Y₀)/t.

Here,

g is the growth rate
Y_t is the population at the end of the period t
Y₀ is the initial population
T is the time period and here, it is 1.

Apply the formula below in cell C3 to find the growth from 2021,

=LN(B3/B2)/(A3-A2).

Step 2: Press Enter. Drag the formula till C5 and format the column as a percentage.

Now, you’ve got a logarithmic view of the population growth. This can be very useful for understanding the growth over time.

Important Things to Note

The value argument used in LN in Google Sheets must be greater than 0. If you input a number other than a positive number, it will return an error.
The LN function is used in scientific, engineering, and financial scenarios, especially where you should predict trends by finding the growth or decay.
If you need a logarithm with a different base, such as base 10, you can use the LOG function.
In Google Sheets, use the EXP function to calculate the inverse of LN.

Frequently Asked Questions (FAQs)

What are some errors you would encounter when using the LN function in Google Sheets?

Using the LN Google Sheets function is straight forward. However, you may encounter the following errors.

The #VALUE! error is displayed if the cell you’re referencing doesn’t contain a number. Check if the value entered ins a number and not a text string or a blank cell.
The #NUM! error occurs when you are trying to find the logarithm of a zero or negative number. Logarithms require positive numbers; they do not exist for negative numbers.

What are the uses of LN in Google Sheets?

The LN function is commonly used in exponential growth or decay scenarios. It can be used to find the population growth, radioactive decay of an element, and compound interest. These involve calculations of time or rate calculation based on continuous growth or decay.

Some of the other uses of LN include:
• Normalizing data
• Making relationships between variables linear.

Can the LN function find the logarithm with a base other than e?

No, the LN function in Google Sheets calculates the natural logarithm (base e) alone. TO find the logarithm with a different base, such as 10, you must use the LOG function. For example, to find the logarithm of a number of base 10, you use:

=LOG(100).
This function returns 2.

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This article must be helpful to understand LN In Google Sheets, with its formula and examples. You can download the template here to use it instantly.

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LN in Google Sheets