Math / Algebra / Functions
Calculate log base 10, natural log (ln), log base 2, or any custom base logarithm from a single value.
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2.000000
log₁₀(100)
100
Antilog (verification)
4.605170
Natural log (ln)
Logarithms
A log calculator finds logarithms in common forms such as log base 10, natural log, and custom-base logs. It is a useful algebra calculator and scientific calculator because logarithms reverse exponential growth and make multiplication-based relationships easier to compare and solve.
A logarithm answers the question: what exponent produces this value? For example, log base 10 of 100 is 2 because 10^2 equals 100. Natural log, written ln, uses the constant e as its base and appears constantly in growth, decay, probability, and calculus.
That is why a log calculator is effectively an inverse exponent calculator. Exponents move from base and power to a final value. Logarithms move from base and final value back to the power required to get there.
Common logarithm and natural log are special cases of the same general idea. A custom-base log simply replaces the default base with another positive value that is not equal to one.
log_b(x) = y if and only if b^y = x
This is the core definition of a logarithm: it gives the exponent y needed to turn base b into x.
ln(x) = log_e(x)
Natural logarithm uses the constant e as its base.
log_b(x) = ln(x) / ln(b)
The change-of-base formula lets you calculate a logarithm in any valid base.
Logarithms appear anywhere growth or scaling is multiplicative rather than additive. They are used in finance for continuous compounding, in science for orders of magnitude, in statistics for transformed data, and in computer science for algorithms and binary scaling.
A simple online log calculator is therefore more than a classroom tool. It helps with formula rearrangement, graph interpretation, and quick verification of exponent problems. That makes it a practical online maths tool for both study and applied calculation.
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