Log Calculator
Calculate log10, ln, or log base b. Enter a value (> 0) and optionally a base (b > 0, b ≠ 1).
Custom base uses the change-of-base formula: logb(x) = ln(x) / ln(b).
Must be > 0 for real logarithms.
Privacy: calculations run locally in your browser. No inputs are stored or transmitted.
How it works
Definitions:
log10(x) = log10(x)
ln(x) = loge(x)
Change of base: logb(x) = ln(x) / ln(b)
Examples
- log10(100) = 2
- ln(e) = 1
- log2(8) = 3
- log0.5(2) = −1
FAQ
- What is a logarithm?
A logarithm answers: “What exponent do I raise the base to, to get the value?” For example, log10(100) = 2 because 10^2 = 100.
- What is ln?
ln(x) is the natural logarithm: log base e (e ≈ 2.71828).
- What inputs are allowed?
The value must be greater than 0. The base must be greater than 0 and not equal to 1. These are required for real-number logs.
- Can I calculate log base 10 and ln quickly?
Yes. Use the preset mode (log10 or ln), then enter the value.
- What is the change-of-base formula?
log_b(x) = ln(x) / ln(b). This calculator uses that identity for custom bases.
- Does this support complex numbers?
No. This tool is for real-number logarithms only.