# Log Calculator

Log Calculator is an online tool that helps to calculate the log value for a given base and argument. It can be thought of as the inverse function of exponentiation. Logarithmic functions help to simplify calculations.

## What is Log Calculator?

Log Calculator helps you to calculate the log value of the given expression. Logs are another way of representing or writing exponential expressions. Logs are widely used in measuring the intensity of earthquakes, the brightness of stars, etc. To use the **log calculator**, enter the values in the given input boxes.

**NOTE: **Enter the values up to three digits only

### Log Calculator

## How to Use Log Calculator?

Please follow the below steps to find the log value using the online log calculator:

**Step 1:**Go to Cuemath's online log calculator.**Step 2:**Enter positive numbers in the given input box.**Step 3:**Click on the**"Calculate"**button to find the value of the log.**Step 4:**Click on the**"Reset"**button to clear the fields and enter new values

## How Does Log Calculator Work?

We can say that the logarithm of a number (say a) is the exponent or power to which a base (say b) must be raised in order to get the number itself.

In exponential form, this can be written as follows

b^{x} = a

Here, b is the base. It is raised to the exponent x. The value of this expression is given by a. Now if we convert this equation by using the log notation, we get

\(log_{b}a = x\)

a, b and x are positive real numbers. a is known as the argument while b is the base.

There are different categories of logarithmic functions depending upon the value of the base. They are:

**Common Logarithmic Functions:** When logarithmic functions have a base of 10 they are known as common logarithmic functions. Usually, such logs do not have 10 written as their base.

10^{2} = 100 \({\Rightarrow }\) log 100 = 2

If the logarithm does not have a base, we can assume it to be 10.

**Natural Logarithmic Functions**: Such types of logs have the base e. e is a mathematical constant and is approximately equal to 2.718. Natural logs are usually represented by ln.

e^{x} = m \({\Rightarrow }\) ln m = x

## Solved Examples on Log Calculator

**Example 1:**

Find the logarithm value of \(log_{2}4\) and verify it using the log calculator.

**Solution:**

\(log_{b}a\) = x ⇔ b^{x} = a

\(log_{2}4\) = x

2^{x} = 4

x = 2

Therefore, the logarithm value of \(log_{2}4\) is 2

**Example 2:**

Find the logarithm value of \(log_{3.2}1\) and verify it using the log calculator.

**Solution:**

\(log_{b}a\) = x ⇔ b^{x} = a

\(log_{3.2}1\) = x

3.2^{x} = 1

x = 0

Therefore, the logarithm value of \(log_{3.2}1\) is 0

Similarly, you can try the log calculator to find the logarithm value of

- \(log_{5.1}25\)
- \(log_{15}45\)

**ā Math Calculators:**

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