O guia abaixo ainda não está disponível em português e é apresentado em inglês. A calculadora está totalmente traduzida.
Como usar esta calculadora
- Enter a positive number x.
- Choose the base, or enter a custom base (positive and not 1).
- Read log_b(x) together with ln, log₁₀ and log₂ of the same number.
Fórmula
A logarithm answers: to what power must the base be raised to get x? Any base can be computed with the change-of-base formula.
log_b(x) = y ⇔ bʸ = x
log_b(x) = ln(x) / ln(b)
log(xy) = log x + log y; log(xⁿ) = n log x
Examples
- log₁₀(1000) = 3 because 10³ = 1000.
- log₂(8) = 3; ln(e²) = 2.
- log₅(125) = ln 125 / ln 5 = 3.
Perguntas frequentes
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, so these logs are undefined in the real numbers.
What is the natural logarithm?
ln(x) is the logarithm base e ≈ 2.71828. It arises naturally in continuous growth, calculus and probability.
Where are logarithms used?
The decibel and pH scales, earthquake magnitudes, compound-interest time calculations and algorithm complexity all use logarithms.