Logarithm Calculator
Calculate log base 10, natural log (ln), log base 2, or any custom base. Step-by-step result with notation.
Logarithm
log(1000) =
3
Frequently Asked Questions about the Logarithm Calculator
What is a logarithm?
The exponent you raise a base to in order to get a number. log_10(1000) = 3 because 10^3 = 1000.
What is ln?
The natural logarithm, base e (about 2.71828). Used in calculus, physics, and continuous compounding.
Why can't log of zero exist?
Because no power of a positive base equals zero. The function approaches negative infinity as the input approaches zero, and is undefined at zero itself.
Why can't the base be 1?
1 raised to any power is 1, so a base-1 log only has a value for the input 1 (any answer works). It is mathematically degenerate, so calculators reject base 1.
How do I change the base?
log_b(x) = ln(x) / ln(b) = log(x) / log(b). Use any natural or base-10 log and divide.