Instantly calculate the logarithm of a number in any base, plus the natural logarithm (ln), base-10 and base-2 logs.
Enter values
A logarithm answers: to what power must the base be raised to get the value?
log₍10₎(1,000) = 3
log₍10₎(1,000) = 3Standard mathematical formulas. Instant in-browser calculation, no account. Exact results for the values you enter.
A logarithm answers: to what power must the base be raised to get the value? It is computed with the change-of-base formula:
log₁₀(1000) = 3, because 10³ = 1000. ln(e) = 1. log₂(8) = 3, because 2³ = 8.
The logarithm of a number in a given base is the power the base must be raised to in order to get the number. log₁₀(1000) = 3, because 10³ = 1000.
Enter the value and set the base to 10 (or press “base 10”). log₁₀(100) = 2.
It is the logarithm in base e ≈ 2.718. ln(e) = 1, ln(1) = 0. It appears often in exponential growth and compound interest.
It answers “how many times do we double?”. log₂(8) = 3, because 2³ = 8. It is used in computer science.
The change-of-base formula: log_b(x) = ln(x) ÷ ln(b). This lets you compute any base using the natural logarithm.
No real power of a positive base yields zero or a negative number, so the logarithm is only defined for strictly positive values.
For logarithmic scales: pH, decibels (sound), earthquake magnitude (Richter) and algorithm complexity.
The logarithm of 1 is always 0 (any base to the power 0 = 1), and the logarithm of the base in itself is 1.