log₁₀ 1000
= 3, because 10³ = 1000.
Logarithm Calculator
Calculate logarithms in base 10, e, 2 or any base, with ln, log₁₀ and log₂ side by side.
Result
Enter your values and select Calculate to see the result.
Runs in your browser — nothing you enter is sent to a server.
How the Logarithm Calculator works
A logarithm answers “what power of the base gives this number?”. Enter the number and choose base 10, e (the natural log, ln), 2 or any other base. The result also shows ln, log₁₀ and log₂, and a check that raises the base to the answer.
Formula
logb(x) = ln x ÷ ln b
x must be positive; the base must be positive and not 1.
Examples
log₂ 8
= 3, because 2³ = 8.
Frequently asked questions
What is ln?
The natural logarithm, with base e ≈ 2.71828. It appears in growth, decay and calculus.
Why can't I take the log of 0 or a negative number?
No real power of a positive base gives 0 or a negative number.
Where are logs used?
Decibels, pH, earthquake magnitudes, compound interest and algorithm speeds are all logarithmic.
Related tools
Scientific Calculator
An online scientific calculator with trigonometry, logarithms, powers, roots, factorials and history.
Math Tools
Quadratic Equation Solver
Solve ax² + bx + c = 0 with real or complex roots, the discriminant and the vertex, with working.
Math Tools
Scientific Notation Converter
Convert numbers to and from scientific, E and engineering notation, exactly.
Math Tools
Half-Life Calculator
Solve radioactive decay problems: amount remaining, initial amount, time elapsed or half-life.
Science Tools