This Log Calculator (Logarithm) helps you to calculate the logarithm of a number with a random chosen base in the domain of a log function.

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. Also, to add, substract or multiply logarithms, head to Condense Logarithms Calculator, and if you want to learn more about logarithms with base 2, you can see our Log Base 2 Calculator.

What is a log (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:

y = \log_bx

If b and x are positive numbers, the product is always a real number y.

To find the inverse value of the logarithm function, there is the Antilog Calculator which does one of the most important calculations in math.

x = \log_b^{-1}(y)=b^y

Here you can see that the exponential function is also used. Learn more about with our Exponent and Dividing Exponents Calculators.

The base of the logarithm is called the decimal or common logarithm. The natural logarithm has the number e as its base. There is our Change of Base Formula, where you can learn more about the base of the logarithm and its properties.

The natural logarithm and the common logarithm

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

log N or log10 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., 10x = 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 \rightarrow \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

82 = 64

log 8 64 = 2

log base 8 of 64

103 = 1000

log 1000 = 3

log base 10 of 1000

100 = 1

log 1 = 0

log base 10 of 1

252 = 625

log 25 625 = 2

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:

\log_b(xy)=\log_b x + \log_b y

Other Calculators

CalCon is a diverse database of calculators, so there are different tools that can help you, such as Square Root Calculator and Cofunction Calculator for you to learn more about roots and trigonometric functions. Related to this subject there is Significant Figures post, to learn more about this subject, but also don’t miss this Linear Equation as well.