Logarithm Calculator

Number (x) Custom base (b)

log₁₀(x)-

ln(x)-

log₂(x)-

log_b(x)-

How it works

The logarithm of x to base b answers the question: what power do I raise b to in order to get x? Since 10³ = 1,000, log₁₀(1000) = 3. The natural logarithm ln uses the base e = 2.71828..., and log₂ is common in computing. Any base can be computed with the change of base formula: log_b(x) = ln(x) / ln(b).

FAQ

Why can't I take the log of zero or a negative number?

No real power of a positive base ever produces 0 or a negative number, so the logarithm is undefined for x ≤ 0.

What is the log of 1?

Always 0, because any base to the power 0 equals 1.

What is the difference between log and ln?

"log" usually means base 10 (or base 2 in computer science); "ln" always means base e.