## Log calculator

In this calculator, we will explain and make it easier for you to calculate **logarithms**. In the text below, we have explained the basic things about logarithms and the history of logarithms themselves.

## What is a logarithm?

The logarithm represents the **inverse function** of potentiation. This implies that the log of a given number *x* is the type to which the second fixed number, base *b*, needs to be raised to deliver that number *x*. Potentiation allows each positive number as a base to have any real power and always gives a positive result. We can represent this as *log*_{b} *(x).* If b and *x* are positive numbers, the product is always a real number *y*.

The base of the logarithm is called the decimal or common logarithm. The natural logarithm has the number *e* as its base.

## The natural logarithm and the common logarithm

The base of a **common** logarithm is always 10. The common log of a number N is written as follows:

**log N or log _{10} N** Decadic logarithms, and decimal logarithms are other names for common logarithms.

If log N = x, then this logarithmic form may be represented in exponential form, i.e., 10 x = N.

**Common **logarithms are widely used in research and engineering. These logarithms are also known as Briggsian logarithms because British mathematician Henry Briggs invented them in the 18th century. For example, a substance’s acidity and alkalinity are represented in exponential terms.

The **natural **logarithm of a number N is the power or exponent by which ‘e’ must be raised to equal N. The Napier constant, denoted by the letter ‘e,’ is approximately equal to 2.718281828.

*N = e x is the same as ln N = x.*

Natural logarithms are most commonly employed in pure mathematics, such as calculus.

The fundamental characteristics of natural logarithms are the same as those of all logarithms.

## Logarithmic functions examples

8 |
log |
log base 8 of 64 |

10 |
log 1000 = 3 |
log base 10 of 1000 |

10 |
log 1 = 0 |
log base 10 of 1 |

25 |
log |
log base 25 of 625 |

## History of the logarithm

John Napier first mentioned **logarithms **in 1614 as a result of simple calculations. Over time, scientists, engineers, and surveyors have improved it to facilitate high-precision calculations. Using logarithm tables, table searches, and a less complex extension can replace plotted multi-digit duplication steps. This is conceivable in light of the reality – which is significant in itself – that the logarithm of an object is the sum of the logarithms of the variables:

Today, all credit for logarithms goes to the scientist Leonhard Euler, who put them together exponentially in the 18th century, who also introduced the letter *e* as the basis for natural logarithms.

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