Log Calculator
Calculate logarithms with any base — common (base 10), natural (base e), binary (base 2) or any custom base.
How to use the Log Calculator
- Enter your inputs into the Log Calculator above.
- Results update instantly as you type — no submit button needed.
- Adjust any value to see how the result changes in real time.
The logarithm definition
log_b(x) = y ⟺ b^y = x · · · Change of base: log_b(x) = ln(x) / ln(b)
The logarithm of x with base b is the exponent to which b must be raised to produce x. Use change-of-base to compute any-base logs from natural or common logs.
Worked example
log₁₀(1000) = 3 (because 10³ = 1000). log₂(64) = 6 (because 2⁶ = 64). ln(7.389) ≈ 2 (because e² ≈ 7.389). log₅(125) = 3 (because 5³ = 125).
Frequently asked questions
What's the difference between log and ln?
log usually means log₁₀ (common log, base 10). ln means log_e (natural log, base e ≈ 2.718). Both are widely used; context determines which.
Why is log of a negative number undefined?
There's no real exponent that makes a positive base produce a negative result. Complex logarithms exist for negative numbers but introduce imaginary components.
What is log of 1?
Always 0, regardless of base — because any base raised to 0 equals 1.