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 log3(81) = 4.

Logarithm examples

Example 1: What is log2(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 log2(256) is 8.

Example 2: What is log7(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 log7(343) is 3.

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 43? 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 log4(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)log10(1000)

How to use the logarithm calculator?

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

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

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Visual Paradigm Tabular

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