## What is Logarithm:

A logarithm expresses power, that is, **indicates the exponent by which the base must be raised to obtain the indicated power**.

To express, for example, a logarithm of 9 in base 3 that is equal to 2 would be:

The expressed logarithm means that 3 raised to 2 is equal to 9:

In this way we can make the correlation between a logarithm and the potentiation being the following equivalent terms:

- exponent = logarithm
- power = number
- Base of the power = base of the logarithm

When the base of the logarithm does not appear to be expressed, it is assumed to be 10 and they are called **logarithms decimals**.

When the base of the logarithm is e, a mathematical expression that indicates 2.718281828, it is called a **natural or natural logarithm**.

## Properties of logarithms

Logarithms have a few properties to consider to make them easier to solve:

There are no logarithms:

- For a number with a negative base,
- From a negative number,
- From zero (0).

The logarithm:

- of 1 is equal to 0.
- from to based on is equal to 1.
- based on a power based on is equal to the exponent.
- of a product is equal to the sum of the logarithms of the factors.
- of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.
- of a power is equal to the product of the exponent times the logarithm of the base.
- of a root is equal to the quotient between the logarithm of the radicand and the index of the root.

## logarithm and algorithm

Logarithm should not be confused with algorithm. Logarithm is a mathematical expression and the algorithm is a set of simple instructions for solving a problem.

See also Algorithm.