What does logarithm mean?
A logarithm is the exponent to which a base must be raised to produce a particular number. In the expression log_b(x) = y, the value y is the logarithm of x to base b; equivalently, b^y = x. Logarithms are useful because they convert multiplication into addition, making it easier to simplify equations, analyze exponential growth, and work with quantities that vary across many orders of magnitude. The common logarithm uses base 10, while the natural logarithm uses base e and is especially important in calculus, differential equations, and models of continuous change. The term is also abbreviated to “log” in technical contexts. Although the idea may seem abstract, it underlies scales used for acidity, loudness, information, and the magnitude of earthquakes.
nounIn mathematics, a logarithm is the exponent to which a given base must be raised to produce a specified number. The expression log_b(x) = y means that b raised to the power y equals x, where b is positive and not equal to 1.
- A mathematical quantity representing the exponent to which a specified base must be raised to obtain a given number.
- The exponent itself in logarithmic notation, as in log₂(8) = 3.
"Taking the logarithm of both sides simplified the equation into a more manageable form."
"The common logarithm of 100 is 2 when the base is 10."
"Scientists often use the natural logarithm when analyzing rates of change."
The plural is used when referring to multiple logarithmic values or mathematical functions.
"The table lists the logarithms of several common values."
A logarithm turns multiplication into addition, making it one of mathematics’ most powerful shortcuts for handling enormous numbers.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does logarithm come from?
The word comes from Greek logos, meaning “ratio” or “proportion,” and arithmos, meaning “number,” together referring to a ratio of numbers. Logarithms were developed as a mathematical method for carrying out certain calculations more efficiently in the 17th century, with John Napier introducing the method and publishing his work on logarithms in 1614. The modern function notation and the widespread use of common and natural logarithms developed through later mathematical practice.
Related word forms
How logarithm is actually used
The abbreviated form “log” is common in mathematics, but the base must be specified when its value matters. The term is specialized and primarily used in mathematics, science, computing, and finance.
Easily confused with logarithm
A logarithm is the mathematical function that gives an exponent, whereas a log may refer to that value informally or to a record in a computer system or journal.