# Logarithm Calculator

This is a logarithm calculator (aka. log calculator) that helps you calculate the logarithm of a number with a chosen base number. Besides, it also tells you what a logarithm is with examples.

## What is a logarithm?

The logarithm is a mathematical function that answers: “How many of one number do we multiply to get another number?”.

For example, how many 3s do we need to multiply to get 81? The answer is 4 because “3 * 3 * 3 * 3 = 81”, which means that we had to multiply 3 four times to get 81. And thus, we say the logarithm is 4, and this can be express as `log`

._{3}(81) = 4

## Logarithm examples

Example 1: What is `log`

_{2}(256)?

We are asking “how many 2s need to be multiplied to get 256”. Since 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 256, we need 8 2s to get 256, so the answer of `log`

is 8._{2}(256)

Example 2: What is `log`

_{7}(343)?

We are asking “how many 7s need to be multiplied to get 343”. Since 7 * 7 * 7 = 343, we need 3 7s to get 343, so the answer of `log`

is 3._{7}(343)

## Logarithm and exponent

The logarithm is the inverse function of exponentiation. Exponents and Logarithms are related, let’s find out how.

The exponent calculates the result of multiplying a number (i.e. a base number) in a given number of times. For example, what’s the result of 4^{3}? The answer is 64 because of 4 * 4 * 4 = 64.

Logarithm counts the number of occurrences of a number in getting a result. In this example, we say the logarithm of 64 with base 4 is equal to 3 `log`

._{4}(64) = 3

As a summary, if b raised to power x gives z, then the logarithm of z with base b is equal to x,

## Logarithm without a base?

Sometimes a logarithm is written without a base, like this: log(1000). This usually means that the base is 10, and is called a **common logarithm**, so:

`log(1000)`

= `log`

_{10}(1000)

## How to use the logarithm calculator?

To use our logarithm calculation tool (log calculator), walk through the steps below:

- Let’s say you want to find the logarithm of 100. Enter 100 in the first field
- Enter the base.
- Check the result.