Logarithm Calculator

Calculate the logarithm of a number for any base.

  • Free to use
  • Accurate results
  • No registration required
  • Works on all devices
Enter a value and base to calculate the logarithm.

Your result

3

Result

AI explanation

Formula

log_base(value) = ln(value) ÷ ln(base)

Worked example

log base 10 of 1000

Worked example: log base 10 of 1000
FieldValue
Value1000
Base10
Result3

Assumptions

  • Both value and base must be positive, and base cannot be 1 (logarithms are undefined in those cases).

Frequently asked questions

What does log base 10 of 1000 equal?

3 — because 10³ = 1000.

What is a common base to use?

Base 10 (common logarithm) and base e ≈ 2.71828 (natural logarithm) are the most common — see the Natural Log Calculator for base e specifically.

Why can't the base be 1?

Any power of 1 equals 1, so log base 1 can't represent any other value — the logarithm is undefined for that base.

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