Logarithm Calculator
Enter a number and a base to calculate its logarithm.
Last updated: September 22, 2026
Frequently asked questions
What is log base 2 of 8?
3 - because 2³ = 8. A logarithm answers "what power do I raise the base to, to get this number?"
How do I calculate a logarithm in a base my calculator doesn't have a button for?
Use the change-of-base formula: logᵦ(x) = ln(x) / ln(b), or equivalently log₁₀(x) / log₁₀(b) - divide the natural log (or log base 10) of your number by the natural log (or log base 10) of your desired base.
What's the difference between ln and log?
"ln" always means natural log (base e ≈ 2.71828). Plain "log" usually means base 10 in everyday math, though in computer science and some fields it can mean base 2 - this calculator shows all three (your chosen base, natural log, and log base 10) to avoid ambiguity.
Why can't I take the log of a negative number or zero?
No real power of a positive base ever produces zero or a negative result, so log(x) is undefined for x ≤ 0 in the real numbers - logarithms of negative numbers require complex numbers, outside what this calculator handles.
What is log base 10 of 1000?
3 - because 10³ = 1000. This calculator also shows the natural log (ln 1000 ≈ 6.9078) alongside it so you can compare bases at a glance.
Can the base of a logarithm be 1 or negative?
No - the base must be a positive number other than 1. A base of 1 always gives 1 raised to any power, which is always 1, so it can never equal your target number (except 1 itself), and negative bases produce inconsistent results for fractional exponents.
Is 'log' the same as 'antilog'?
No, they're inverses. Log finds the exponent that produces a number (log₂8 = 3), while antilog does the reverse - it raises the base to a given exponent (antilog base 2 of 3 = 2³ = 8). This calculator computes the log direction only.