Logarithm Calculator
log base 10, e, 2 or any base, with the antilog, the exact power when there is one, the change-of-base working and the product, quotient and power laws.
log_b(x) together with ln, log₁₀ and log₂ of the same x, b^y for a y you enter, the exact exponent when x is a power of the base, the change-of-base line and the log laws with your numbers.
Example: log₁₀ 1 000 = 3 exactly; log₂ 8 = 3 and 2¹⁰ = 1 024; log₅ 20 = ln 20 ÷ ln 5 = 2.9957 ÷ 1.6094 = 1.8614; log₂(8 × 4) = 3 + 2 = 5.
One identity
covers every base.
How any base is computed, what the exact-power check does, and the log laws.
Change of base
log_b(x) = ln x ÷ ln b for any positive base other than 1; log₁₀ and log₂ use the dedicated functions for the last bit of precision. The line shows the identity with your numbers so the arithmetic can be checked on a calculator.
Exact powers and antilog
When bᵏ equals x for an integer k (within double-precision tolerance) the page says so — log₁₀ 1 000 = 3 exactly, not 2.9999999999999996. The antilog b^y is the inverse operation for a y you enter.
The laws
With a second argument z the product, quotient and power laws are written out: log(xz) = log x + log z, log(x/z) = log x − log z, log(x^z) = z·log x. Results are double precision (about 15 significant digits) and rounded to the places you choose; x ≤ 0 has no real logarithm and is refused. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- log_b(x) = ln x ÷ ln b; laws log(xy) = log x + log y, log(x/y) = log x − log y, log(xⁿ) = n log x; double-precision evaluation (≈ 15 significant digits)
Last reviewed 21 September 2026. How results are checked: How we verify.