Meaning of Logarithm

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:

logarithm of 9

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

three raised to two

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.
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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.