Compute logarithms in any base, plus natural log and antilog.
The logarithm log_b(x) answers 'b to what power equals x?'. The natural logarithm ln(x) uses base e ≈ 2.71828. The common logarithm log₁₀(x) is standard in engineering. The binary logarithm log₂(x) is central to computer science. The antilogarithm (antilog) is the inverse: it raises the base to the given power, 'undoing' the logarithm.
Definition
log_b(x) = y if and only if b^y = x
Change of base
log_b(x) = ln(x) / ln(b)
Antilogarithm
antilog_b(x) = b^x
3. Because 2³ = 8. In general, log₂(2ⁿ) = n.
In science and engineering, 'log' without a base usually means log base 10. In mathematics, it often means the natural logarithm (ln). This calculator makes the base explicit to avoid ambiguity.
Because no real power of a positive base equals zero. As the argument approaches 0 from the right, log_b(x) approaches −∞, so 0 is a boundary where the function diverges.
10³ = 1000. The antilog undoes the log: log₁₀(1000) = 3 and 10³ = 1000 are two ways of saying the same thing.