Logarithm meaning (what is it, concept and definition)

What is Logarithm:

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

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

The logarithm expressed means that 3 raised to 2 equals 9:

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

• Exponent = logarithm Power = base number of the power = base of the logarithm

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

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

Properties of logarithms

Logarithms have some properties that must be taken into account to make them easier to solve:

There are no logarithms:

• From a negative-based number, From a negative number, From zero (0).

The logarithm:

• of 1 is equal to 0. of a in base a is equal to 1. in base a of a power in base a 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 by 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.