Mathematics · Glossary
What is Logarithm?
Quick definition
The exponent to which a base must be raised to produce a given number. log(100) = 2 means 10² = 100.
Full explanation
A logarithm is the inverse of exponentiation. The logarithm of N to base b is the power to which b must be raised to equal N. If b^x = N, then log_b(N) = x. Common logs use base 10 (log); natural logs use base e ≈ 2.718 (ln). Logarithms compress huge ranges into manageable numbers: log(10) = 1, log(1,000,000) = 6. The Richter scale, decibels, pH, and information theory all use logarithmic scales. Logarithm properties (product → sum, power → multiplication) were used to turn multiplication into addition before calculators existed. Today they are essential in finance (CAGR), machine learning, and physics.
Related calculators
Calculators that use or explain Logarithm.
Related terms
More from Mathematics
Standard Deviation
A measure of how spread out numbers are from their mean. Low = consistent, high = volatile.
P-Value
The probability of observing results at least as extreme as those observed, assuming the null hypothesis is true.
Mean (Average)
The sum of values divided by the count. The most common type of "average." Sensitive to outliers.
Median
The middle value in a sorted list. Half the values are above, half below. Robust to outliers.
Pythagorean Theorem
In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs: a² + b² = c².
Exponent
A number that indicates how many times a base is multiplied by itself. 2³ = 2×2×2 = 8.
Last reviewed: June 15, 2026 • Category: Mathematics