# Excel LOG function

## What is LOG function in Excel?

The LOG function is one of the math functions of Excel.

It Returns the logarithm of a number to the base you specify.

We can find this function in Math & trig category of insert function Tab.

## How to use LOG function in excel

1. Click on an empty cell (like F5 )

2. Click on the fx icon (or press shift+F3)

3. In the insert function tab you will see all functions

4. Select math and trig category

5. Select LOG function

6. Then select ok

7. In the function arguments Tab you will see LOG function

8. Number is the positive real number for which you want the logarithm

9. Base is the base of the logarithm; 10 if omitted

10. You will see results in the formula result section

## Examples of LOG function in excel

1. `=LOG(100)` returns the natural logarithm of 100, which is approximately 4.605.
2. `=LOG(10, 100)` returns the logarithm of 100 with base 10, which is equal to 2.
3. `=LOG(A2)` assumes cell A2 contains a number, and returns its natural logarithm.
4. `=LOG10(100)` returns the base-10 logarithm of 100, which is equal to 2.
5. `=LOG(2, 8)` returns the logarithm of 8 with base 2, which is equal to 3.
6. `=LOG(A2, A3)` assumes cells A2 and A3 contain numbers, and returns the logarithm of A3 with base A2.
7. `=LOG(E3)/LOG(E4)` assumes cells E3 and E4 contain numbers, and returns the logarithm of E3 divided by the logarithm of E4 (this is a common way to calculate the base of a logarithm).
8. `=LOG(A2)*B2` assumes cell A2 contains a number, and multiplies its natural logarithm by the value in cell B2.
9. `=LOG(1.5)` returns the natural logarithm of 1.5, which is approximately 0.405.
10. `=LOG(-10)` returns an error, because the natural logarithm is only defined for positive numbers.

Example :

### How to use LOG function in Excel

You can see examples of LOG function below:

``````log(A2,B2) ----->>>>answer is  3

## Uses of LOG function in Excel

### Excel LOG Function: Understanding the Syntax

The syntax for the LOG function in Excel is as follows:

=LOG(number, [base])

The “number” argument is the positive real number for which you want to find the logarithm. The “base” argument is optional and represents the base of the logarithm.

For example, if you want to find the logarithm of 10 to the base 2, you can use the following formula:

=LOG(10,2)

### Excel’s LOG Function and its Base Argument: What You Need to Know

The base argument in Excel’s LOG function specifies the base of the logarithm. If it is not specified, the function calculates the logarithm to base 10 by default.

For example, if you want to find the logarithm of 8 to base 2, you can use the following formula:

=LOG(8,2)

The result will be 3, since 2^3 = 8.

### How to Use Excel’s LOG Function to Find the Logarithm of a Number

To use Excel’s LOG function to find the logarithm of a number, simply enter the number as the first argument and the base (if other than 10) as the second argument.

For example, if you want to find the logarithm of 25 to base 5, you can use the following formula:

=LOG(25,5)

The result will be 2, since 5^2 = 25.

### Handling Negative Numbers with Excel’s LOG Function

Excel’s LOG function cannot handle negative numbers because there is no real logarithm for a negative number. Attempting to calculate the logarithm of a negative number will result in an error.

For example, if you want to find the logarithm of -1, you should expect to see an error when using the LOG function.

=LOG(-1)

This will result in a #NUM! error.

### Using Excel’s LOG Function for Natural Logarithms

To calculate natural logarithms using Excel’s LOG function, use “e” or “Euler’s number” as the base argument. For example:

=LOG(10,E())

This will give you the natural logarithm of 10.

### LOG vs LN Functions in Excel: Know the Difference

The LOG function in Excel calculates the logarithm of a number to a specified base, while the LN function calculates the natural logarithm of a number. In other words, the LOG function allows you to specify any base, while the LN function always uses Euler’s number as the base.

For example, to find the natural logarithm of 100 using the LN function, enter:

=LN(100)

To find the logarithm of 100 to base 10 using the LOG function, enter:

=LOG(100,10)

### Excel’s LOG Function with Cell References: Step-by-Step Guide

To use Excel’s LOG function with cell references instead of numbers, simply replace the number argument with the cell reference. For example:

=LOG(A1,B1)

This will give you the logarithm of the number in cell A1 to the base specified in cell B1.

### Finding Inverse Logarithms with Excel’s LOG Function

To find the inverse logarithm (i.e., the antilogarithm) of a number using Excel’s LOG function, use exponentiation. The inverse logarithm of a number can be found by raising the base to the power of the logarithm of the number. For example:

=10^LOG(100)

This will give you the inverse logarithm (i.e., antilogarithm) of 100.

### Calculating Logarithmic Trendlines in Excel using the LOG Function

Excel’s LOG function can be used to calculate logarithmic trendlines for a set of data points. To do this, you will need to plot the data on a chart and then add a logarithmic trendline.

Excel will automatically calculate the logarithmic equation for the trendline using the LOG function.

For example, if you have a set of data in columns A and B, select the data and create a scatter plot. Then, right click on one of the data points and select “add trendline.”

In the trendline options, select “logarithmic” and Excel will generate the logarithmic equation for the trendline using the LOG function.

### Excel’s LOG Function: Maximum Value Considerations

The LOG function in Excel is used to calculate logarithms to a specified base. However, it is important to note that the function has maximum and minimum value considerations.

When taking the logarithm of a number, the result approaches negative infinity as the input approaches 0. Similarly, as the input approaches infinity, the result approaches positive infinity.

Therefore, it is important to ensure that the input to the LOG function falls within a valid range.

For example, if we want to calculate the logarithm of a number in base 10 using the LOG function, we might use the formula =LOG(100).

This would return the value 2, since 10 raised to the power of 2 is equal to 100. However, if we input a value of 0 or a negative number into the function, an error will be returned.

### Excel’s LOG10 Function: Finding Base-10 Logarithms Made Easy

The LOG10 function in Excel is similar to the LOG function, but it specifically calculates logarithms to base 10. This can be useful in a variety of applications, such as measuring the pH of a solution or analyzing sound levels on a decibel scale.

To use the LOG10 function, simply enter the input value as the argument. For example, if we wanted to find the base-10 logarithm of 100 using the LOG10 function, we could use the formula =LOG10(100). This would return the value 2, since 10 raised to the power of 2 is equal to 100.

### Compound Interest Calculation with Excel’s LOG Function

The LOG function in Excel can also be used to calculate compound interest. To do this, we need to use a modified version of the formula, which takes into account the interest rate, number of periods, and principal amount.

For example, if we wanted to calculate the future value of an investment with a principal amount of \$1000, an annual interest rate of 5%, and a term of 10 years, we could use the formula =1000EXP(10LOG(1+0.05/10))). This would return the value 1628.89, which is the future value of the investment after 10 years at a compound interest rate of 5%.

### Excel’s LOG Function: Whole Number or Decimal Output?

By default, the LOG function in Excel returns a decimal value. However, there may be cases where it is more useful to have the result rounded to a whole number. To do this, we can utilize the ROUND function in combination with the LOG function.

For example, if we wanted to calculate the base-2 logarithm of 32 and round the result to the nearest integer, we could use the formula =ROUND(LOG(32,2),0). This would return the value 5, since 2 raised to the power of 5 is equal to 32.

### Solving Exponential Equations with Excel’s LOG Function

The LOG function in Excel can also be used to solve exponential equations. This involves taking the logarithm of both sides of the equation, which allows us to isolate the exponent.

For example, let’s say we have the equation 2^x = 8. To solve for x, we can take the base-2 logarithm of both sides, like so: LOG(2,2^x) = LOG(2,8). This simplifies to x = LOG(2,8), which we can evaluate using Excel’s LOG function as follows: =LOG(8,2). This returns the value 3, since 2 raised to the power of 3 is equal to 8. Therefore, the solution to the equation 2^x = 8 is x = 3.

### Using Excel’s LOG Function to Compare Values on Different Scales

Excel’s LOG function can be used to compare values that are on different scales. By taking the logarithm of each value, they can be converted to a common scale for easier comparison.

For example, let’s say we want to compare the growth rates of two companies, one with a starting value of \$100 and an ending value of \$200, and another with a starting value of \$10,000 and an ending value of \$20,000. Taking the logarithm base 10 of each ending value, we get:

LOG(200) = 2.301 LOG(20000) = 4.301

Now we can see that the second company had a higher growth rate, despite the larger starting value.

### Calculating dB Level in Excel with the LOG Function

The decibel (dB) level is a measure of sound intensity relative to a reference level. It can be calculated using the following formula:

dB = 10 * LOG(I/I0)

Where I is the intensity of the sound and I0 is the reference intensity. Excel’s LOG function can be used to calculate the dB level of a sound.

For example, let’s say we have a sound with an intensity of 0.001 W/m^2 and a reference intensity of 1e-12 W/m^2. Using the formula above and Excel’s LOG function, we can calculate the dB level:

dB = 10 * LOG(0.001/1e-12) = 120 dB

So the sound has a dB level of 120, which is considered very loud.

### pH Value Calculation with Excel’s LOG Function

The pH value is a measure of the acidity or basicity of a solution. It is defined as the negative logarithm base 10 of the hydrogen ion concentration (pH = -log[H+]). Excel’s LOG function can be used to calculate the pH value of a solution.

For example, let’s say we have a solution with a hydrogen ion concentration of 1e-5 M. Using the formula above and Excel’s LOG function, we can calculate the pH value:

pH = -LOG(1e-5) = 5

So the solution has a pH of 5, which is slightly acidic.

### Entropy Calculation Made Easy with Excel’s LOG Function

Entropy is a measure of the disorder or randomness in a system. It can be calculated using the following formula:

S = -k * Σ(p * log(p))

Where k is the Boltzmann constant, p is the probability of each state, and the sum is taken over all possible states. Excel’s LOG function can be used to calculate the entropy of a system.

For example, let’s say we have a system with two possible states, A and B, with probabilities of 0.7 and 0.3 respectively. Using the formula above and Excel’s LOG function, we can calculate the entropy:

S = -1.38 * (0.7 * LOG(0.7) + 0.3 * LOG(0.3)) = 0.88

So the system has an entropy of 0.88, indicating a moderate level of disorder.

### Troubleshooting Common Errors When Using Excel’s LOG Function

When using Excel’s LOG function, there are a few common errors that may occur. One is the #NUM! error, which occurs when the argument to the logarithm is zero or negative. To avoid this error, make sure that the argument is greater than zero.

Another common error is the #VALUE! error, which occurs when the argument is not a valid number. This can happen if the argument contains text or other non-numeric characters. To fix this error, make sure that the argument is a valid number.