Log (Logarithmic) Calculator

The Log (Logarithmic) Calculator is an online tool that provides the logarithmic result based on the given data. You only need to enter the number for which you want to calculate the logarithm and the base of the logarithm.

You can enter any number that will be the base of the logarithm, such as 2, 3, 10, etc. And if you want to calculate the natural logarithm ln, enter e as the base.

The result of the operation appears immediately after the equals sign.

Decimals (Precision)

log

3.00

select the logarithmic base:

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How do I use the log calculator?

The logarithm calculator calculates the logarithm of a number based on the data you give it: the base of the logarithm and the number for which you want to calculate the logarithm.

All you need to do is enter the base of the logarithm, such as 2, 10 or e (if you want to calculate the natural logarithm), and the number for which you want to know the result.

It is possible to set the precision of the result. From 0 to 10 decimal places.

Logarithm - Definition

For the numbers a and b, where a, b > 0 and a ≠ 1, the logarithm with base a of the number b is called the real number x which satisfies the equation: ax = b.

The logarithm is the inverse of the power of a number.

Decimal Logarithm

The decimal logarithm is also known as the Briggs logarithm. It is a logarithm with a base of 10.

lg x = log 10x, so 10x = 10

The concept of the decimal logarithm was introduced over 400 years ago (in 1614) by the English mathematician Henry Briggs.

Natural Logarithm

The natural logarithm is also known as Neper's logarithm. It is named after the Scottish mathematician John Neper.
It is a logarithm whose base is e.

The number e is Euler's number (a mathematical constant), which is approximately 2.718281828459.

The natural logarithm is denoted by the symbol log_e or simply ln.

Some examples

log₂ 8 = 3, because 2³ = 8,
log 1000 = 3, because 10³ = 1000,
log¹⁰ 0,1 = -1, because 10^-1 = 0,1,

Using logarithms

In mathematics - In the past, logarithms were used to multiply large numbers. Nowadays, they can be found, for example, in graphs (logarithmic scale),
in chemistry - logarithms are used to calculate pH, for example,
in seismology - the Richter scale is a logarithmic scale used to measure the magnitude of an earthquake,
the sound intensity level is given in decibels (dB) and is calculated using a logarithmic function.