Free Logarithm Calculator 2026 — Log and Ln Online
Calculate log (base 10) and ln (natural log base e) instantly. Logarithm definition: log_b(x) = y means b^y = x. Common examples: log(100) = 2 (because 10² = 100), log(1000) = 3 (because 10³ = 1000), ln(e) = 1, ln(1) = 0. Natural log (ln) uses base e ≈ 2.71828 and is used extensively in calculus, exponential growth/decay, and statistics. No sign-up required — your data never leaves your browser. Works instantly on desktop, tablet, and mobile. Completely free with no daily usage limits, no watermarks, and no account needed. Trusted by students, professionals, and businesses worldwide. FixFlowHub is a browser-based toolbox with 120+ free utilities covering PDF, image, text, calculator, and productivity tools.
Frequently Asked Questions
What is the difference between log and ln?
log (common logarithm) uses base 10: log(100) = 2 because 10² = 100. ln (natural logarithm) uses base e (≈2.71828): ln(e) = 1. In mathematics and physics, ln is more fundamental. In engineering and common usage, log base 10 is often assumed when no base is specified.
How do you calculate log without a calculator?
For common values: log(1) = 0, log(10) = 1, log(100) = 2, log(1000) = 3. For other values, use the change of base formula: log_b(x) = ln(x) ÷ ln(b). You can also use the rule: log(a×b) = log(a) + log(b), and log(a^n) = n × log(a).