By Zencalcy Editorial TeamLast reviewed About us
Compute ln, log₁₀, or log of any positive number in any valid base. Custom bases use the change-of-base formula log_b(x) = ln(x)/ln(b); invalid domains get plain explanations, not NaN.
Natural, common, or any custom-base logarithm via change of base.
log_b(x) = ln(x) / ln(b)
| Symbol | Meaning |
|---|---|
| x | Positive number to take the log of |
| b | Base: positive and ≠ 1 (custom mode) |
log₁₀(1000) = 3, ln(e) = 1, and log₂(32) = 5.
Continue with the Percentage Calculator, all math calculators, or browse the full calculator directory.
Real logarithms are undefined for zero and negatives — no power of a positive base yields them.
Click to use the Absolute Value Calculator and get instant results.
Click to use the Basic Calculator and get instant results.
Click to use the Scientific Calculator and get instant results.
Click to use the Exponent Calculator and get instant results.
Click to use the Square Root Calculator and get instant results.
Click to use the Cube Root Calculator and get instant results.
Content updated: September 2026