Logarithm values are often used in various fields, including science, engineering, and finance. In Excel, we can use the** LOG function** to calculate logarithm values. It is categorized as a Math & Trigonometry function in Excel and it is available in all versions of Excel starting from Excel Starter 2007 to Excel for Microsoft 365. Now, in this article, I’ll demonstrate 5 basic and 5 real-life examples of using the **LOG** function in Excel. These examples will include simple logarithmic calculations and various applications of this function in science, engineering, and finance.

The following image depicts an introduction to the **LOG** function.

Now, let’s get started.

**Table of Contents**Expand

## LOG Function in Excel: Syntax

**Summary**

Returns the logarithm of a number to the base you specify. According to mathematics, the logarithm is the inverse of exponentiation. That means the logarithm of any given number is the exponent to which the base has to be raised to get a specified number. For instance, if **x **is the exponent of base** b** to get the value **y**.

**If b**^{x}**=y **Then **log**_{b}**y=x**

**Syntax**

The syntax of the **LOG** function is as follows:

**=LOG(number, [base])**

**Arguments**

Arguments | Requirement | Explanations |
---|---|---|

number |
Required | The positive real number for which we want the logarithm (e.g. 64, 8, 2.1, etc.). This value is numeric and must be greater than zero. |

base |
Optional | This base is used to calculate the logarithm of a number. If this parameter is omitted, the function will use a base of 10. |

**Return Value**

The **LOG** function returns a numeric value.

**Available in**

Excel for Microsoft 365 | Excel for Microsoft 365 for Mac | Excel for the web | Excel 2021 | Excel 2021 for Mac | Excel 2019 | Excel 2019 for Mac | Excel 2016 | Excel 2016 for Mac | Excel 2013 | Excel 2010 | Excel 2007 | Excel for Mac 2011 | Excel Starter 2010

Depending on the nature of the base argument, the logarithm values can be of two types: **common** (or Briggian) logarithms and **natural** (or Napierian) logarithms. While natural logarithms are based on the mathematical constant “**e**“, which is an irrational number approximately equal to **2.71828**, common logarithms are based on other numeric values. Therefore, by changing the base argument alone, we can access a variety of applications.

First, we’ll demonstrate the application of the **LOG** function in a few basic logarithmic calculations by varying the base argument.

## 1. Using LOG Function in Excel with Default Base Argument (Log10)

If we apply the **LOG** function without specifying the base argument, then it is assumed to be **10** by default.

For example, the following formula in **cell D5** will return a 10-based log value of the number in **cell B5**.

`=LOG(B5)`

**Note:**

However, in **Cell** **D10**, we can attain the same results by applying **the LOG10 function** also as it returns 10-based logarithm values.

`=LOG10(B10)`

## 2. Using LOG Function with a Custom Base

Unlike the previous example, if we apply the **LOG** function with both number and base arguments, then it returns the exponent to which the base argument must be raised to produce the number argument.

For example, we have calculated the Log Values of some numbers in the following image. The bases are specified beside the numbers. Just insert the following formula in **cell D5**, and copy this formula to the remaining cells of **Column D** by using the **Fill Handle** icon.

`=LOG(B5,C5)`

## 3. Applying a Decimal Base with LOG Function in Excel

The arguments of the **LOG** function can be varied to a wide range. For example, we can use decimal base arguments in the **LOG** function.

**Read More:** How to Calculate Log Base 2 in Excel

## 4. Combining Excel LOG and EXP Functions to Calculate the Natural Logarithm of a Number

To calculate natural logarithms, we require the irrational number “**e**” as the base argument. This can be accomplished by combining the** EXP function** with the **LOG** function.

In **Cell D5**, insert the following formula and get the required output by pressing the **Enter** key.

`=LOG(B5,EXP(1))`

Here, the **EXP** function returns the exponential of **1** i.e. the irrational number “**e**”, which works as the base for the **LOG** function. Next, the **LOG** function returns the natural logarithm of the provided number.

**Note:**

However, we can apply **the LN function** as a better alternative to this formula. The formula to return the natural logarithm of a number by using the **LN** functions is given below:

`=LN(B10)`

**Read More: **How to Calculate Natural Logarithms in Excel

## 5. Applying Excel Log Function in VBA

We can also implement the **LOG** function in Excel **VBA** to calculate the logarithm of a given number with a specified base. Look at the following dataset where we have a number and a base value stored in **Cell B5** and **C5**.

- To calculate the logarithm of these values, first, we have to go to the
**Developer tab**and select the**Visual Basic**.

- If the
**Developer**tab is not installed in your Excel, you can install it from**File > Options > Customize Ribbon > Main Tabs**directory. - Another way to open the window for inserting
**VBA**code is to use the keyboard shortcut**ALT + F11**.

- After the
**Microsoft Visual Basic for Applications**window opens, from the**Insert**ribbon, select the**Module**option and then insert the following code.

```
Option Explicit
Function LogAny(b As Double, y As Double) As Double
' b: base y: a given number
LogAny = Log(y) / Log(b)
End Function
Sub Log_VBA()
Dim num As Double
Dim base As Double
num = Range("B5")
base = Range("C5")
MsgBox LogAny(base, num)
End Sub
```

- Next,
**Save**and**Run**the module. - A message box like the following will appear where we can see the required output.

## LOG Function in Excel: 5 Real-Life Applications

We have discussed the basic use of the Excel **LOG **function so far. Now, we will learn some real-life applications.

### 1. Use LOG Function to Calculate the Number of Iterations Required to Find a Number (Binary Search)

**Binary search** is a commonly used algorithm in computer science and programming for finding a specific value in a sorted list or array of values.

The algorithm works by repeatedly dividing the search interval in half, comparing the middle value to the target value, and eliminating one-half of the search interval each time, until the target value is found or determined to be not in the list.

For example, consider the following sorted array of 12 numbers:

Now, suppose we want to search for the number **67** from the array.

- The number of iterations required to find this number by using the binary search method is-

**Iteration-1:**

**Iteration-2:**

**Iteration-3:**

- These number of iterations could have been calculated by using a simple Excel formula-

`=ROUND(LOG(12,2),0)`

- This formula simply returns how many times we have to divide the array into halves.
- Now, let’s have a look at the following dataset where we have item counts for a list of arrays.

- We want to calculate the number of iterations required to find any item from these arrays by using a combination of the
**LOG**and**ROUND**functions.

- Type in the following formula in
**Cell C5**and press**Enter**key to get the required result.

`=ROUND(LOG(B5,2),0)`

- Later, use the
**Fill Handle**tool to copy the formula in other cells of**Column C**.

**Formula Explanation:**

**LOG(B5,2)**

First, the **LOG** function returns the 2-base logarithm of the specified items count value.

**ROUND(LOG(B5,2),0)**

Afterward, if the **LOG** function returns a decimal number, then the **ROUND** function rounds the number to **0** decimal digits.

### 2. Apply LOG Function in Evaluation of Annualized Return on Investment (ROI) for Continuous Compounding

**Return on Investment** (**ROI**) is a financial parameter that enumerates the profitability of an investment relative to its cost.

The annualized ROI value under continuous compounding can be described as below-

Here, the **Initial Value** represents the Investment made on any stock and the **Ending Value** represents the summation of the Investment made and the value returned from the investment after **t **years.

Now, let’s have a look at the following dataset where we have investment, return, and number of years to get the return listed for several stocks.

From here, we want to enumerate the annualized ROI value for each stock so that we can find potential stocks for investment.

- For that, insert the following formula in
**Cell F5**and press the**Enter**key.

`=LOG((C5+D5)/C5)/E5`

- Later, drag the
**Fill Handle**icon down to copy the formula in the remaining cells of**Column F**.

### 3. Find the Nature of Chemical Solutions Using IF, LOG and POWER Functions

The nature of any chemical solution can be determined from its PH value and the PH values can be calculated using the **LOG** function in Excel.

If the **PH < 7**, then the solution is of acidic nature, if the **PH > 7**, then the solution is of alkaline nature, and if **PH = 7**, then the solution is of neutral nature.

Now, let’s have a look at our dataset. We have the concentration of Hydrogen ions for a list of chemical solutions. We want to calculate the PH value and nature of these solutions.

Since the concentration values are provided in **μmol/Litre** units, we have to multiply these concentration values by **10**** ^{-6}** while calculating PH values. We require

**the POWER function**along with the

**LOG**function for this purpose.

- So, to calculate the PH values of the solutions, first, type in the following formula in
**Cell D5**and press**Enter**key.

`=-LOG(C5*POWER(10,-6),10)`

- Later, use the
**Fill Handle**tool to copy the formula in other cells of**Column D**.

**Formula Explanation:**

**POWER(10,-6)**

The **POWER** function here is used for returning the value **10**** ^{-6}** (

**10**raised to the power

**-6**).

**-LOG(C5*POWER(10,-6),10)**

This formula returns the negative 10-based logarithm of the Hydrogen ion concentration values i.e. PH values.

- Now, we can determine the nature of the solutions based on these PH values.

- Type the formula below in
**Cell E5**and press**Enter**key to get the required nature of the solution. Then copy this formula down.

`=IF(D5<7,"Acidic",IF(D5>7,"Alkaline","Neutral"))`

**Formula Explanation:**

- Here, the first
**IF function**checks whether the PH value is less than**7**. If the criterion is true, then it returns “**Acidic**”. - Else, the second
**IF**function is executed, which checks whether the PH value is greater than**7**. If this criterion is true, then the second IF function returns “**Alkaline**”. Else, it returns “**Neutral**”.

### 4. Measuring the Magnitude of Earthquakes with LOG Function

The magnitude of an earthquake is a measure of the size or strength of the earthquake. This measure is an important factor in assessing the potential impact and damage of an earthquake. There are several different scales used to measure earthquake magnitude. Here, we’ll use the formula below which is provided by **Seismologist Dr. Hiroo Kanamori**.

Here, **M**** _{0}** is the Seismic Moment and

**M**

**is the Moment Magnitude of any earthquake.**

_{w}To calculate the magnitude of earthquakes, we’ll use the following dataset where we have the Seismic Moments of several earthquakes listed in column **C**.

The values of Seismic Moments are measured in **dyne-cm **units and categorized in **Scientific** format. Now, let’s calculate the magnitude of the listed earthquakes.

- In
**Cell D5**, type in the following formula and press**Enter**key to get the required output.

`=(2*LOG(C5,10)/3)-10.73`

- Later, drag the
**Fill Handle**icon to copy the formula for the remaining earthquakes.

### 5. Using LOG Function to Calculate the Half-Life of Radioactive Substances

The half-life of a radioactive substance is the amount of time it takes for half of the original radioactive atoms to decay. This is an important parameter for understanding the behavior and properties of radioactive materials.

This parameter is widely used in the Nuclear Power Sector, Medical science, Geology, etc. fields. To calculate this parameter, we first have to calculate the decay constant (**k**) by utilizing the variables initial amount (**N**** _{0}**), remaining amount (

**N**), and decay period (

**t**).

After calculating the decay constant, we can enumerate half-life (**T**** _{1/2}**) by using the formula below-

So, let’s have a look at our dataset for this problem. We have got the initial amount (Column **C**), the remaining amount (Column **D**), and the decay period (Column **E**) for several elements listed here.

Now, let’s calculate the half-lives for these radioactive elements.

- First, insert the following formula in
**Cell F5**and press**Enter**key to calculate the decay constant.

`=LOG(C5/D5,EXP(1))/E5`

- Later, drag the
**Fill Handle**icon down to copy the formula in other cells of**Column F**.

**Formula Explanation:**

**EXP(1)**

The **EXP** function returns the exponential of **1** i.e. the irrational number “**e**”, which works as the base for the **LOG** function.

**LOG(C5/D5,EXP(1))/E5**

This formula calculates the natural logarithm of the ratio of the initial amount and the remaining amount of the radioactive substance and divides it by the decay period to calculate the decay constant.

- Afterward, get the half-life value by inserting the following formula in
**Cell G5**and pressing the**Enter**key.

`=LOG(2,EXP(1))/F5`

- Finally, use the
**Fill Handle**tool to copy this formula for the remaining radioactive substances.

## Common Errors with Excel LOG Function

Although the execution of the Excel **LOG** function may seem simple, some common errors can occur if the users provide wrong arguments. Three different types of errors can occur for providing irrelevant arguments.

**Negative or Zero Arguments Return #NUM! Error**

The number and base arguments in the **LOG** function have to be greater than zero. If a negative or zero value is used for any argument, the **LOG** function returns a **#NUM!** error.

**Non-Numeric Arguments Cause #VALUE! Error**

The arguments of the **LOG** function can’t be text values either. If a text value is used for any argument, then the **LOG** function returns **#VALUE!** error.

**#DIV/0! Error Occurs If Base Argument Value Is Equal to 1**

Finally, the base argument value can’t be equal to **1**. If we set the base argument to **1**, then the **LOG** function will return **#DIV/0!** Error.

## Excel LOG vs POWER Function: What Is the Difference?

The **LOG** function is the reverse of the **POWER** function. The **POWER** function is used to raise a number to a given exponent, whereas the **LOG** function can be used to return the same exponent.

- For demonstration, consider the following example where we have
**a base and an exponent**.

- We can apply the following formula using the
**POWER**function to raise the base to the given exponent.

`=POWER(B5, C5)`

- Now if we use the output of the
**POWER**function as the number argument for the**LOG**function, we can return the exponent value. The formula is given below for this operation-

`=LOG(D5,B5)`

## Things to Remember

- If the base argument is omitted while applying the
**LOG**function, then it is assumed to be**10**. - The arguments of the
**LOG**function can’t be negative, zero, or non-numeric. - The base argument of the
**LOG**function can’t be equal to**1**.

## Frequently Asked Questions

**1. Can the LOG function be used to calculate the natural logarithm?**

** Answer:** Yes, the

**LOG**function can calculate natural logarithms. The base argument has to be set to the irrational number “

**e**” for this. We can apply the following formula to calculate the natural logarithms of any number.

**=LOG(number, EXP(1))**

Here, provide the number for which you want the natural logarithm value.

**2. What is the difference between the LOG, LOG10, and LN functions in Excel?**

** Answer:** The syntax and purpose of using the

**LOG**,

**LOG10**, and

**LN**functions are listed below-

Function | Syntax | Output |
---|---|---|

LOG | LOG(number, [base]) | The logarithm of a number based on the specified base |

LOG10 | LOG10(number) | 10-base logarithm values |

LN | LN(number) | e-base logarithm values |

So, the main difference between these three functions is the base of the logarithm that they use. The **LN** function calculates the natural logarithm (base **e**), the **LOG10** function calculates the logarithm to base **10**, and the **LOG** function allows us to specify the base value.

**3. How do I troubleshoot errors that occur when using the LOG function in Excel?**

** Answer:** Here are some tips for troubleshooting errors in formulas that may occur when using the

**LOG**function in Excel:

- Check your syntax: Make sure that you have entered the correct syntax for the
**LOG**Make sure that the syntax is correct and that there are no missing or extra parentheses, commas, or other syntax errors. - Check your arguments: Make sure that the arguments you have provided to the
**LOG**function are valid. - Check for errors in the source data.
- Check your settings: Check your Excel options and make sure that the calculation settings are set to automatic.

By following these tips, you should be able to troubleshoot most errors that occur when using the **LOG** function in Excel.

**Download Practice Workbook**

You may download the following file and practice yourself.

## Conclusion

This concludes our article on the Excel **LOG** function. We demonstrated several examples of using the **LOG **function in fields of science, finance, computer engineering, etc. We hope the demonstrated examples were sufficient for your requirements. Feel free to leave your thoughts on the article in the comment section.

## Excel LOG Function: Knowledge Hub

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