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
When to use this tool
This tool is designed for quick, practical tasks such as everyday calculations, data formatting, or simple conversions. It is best used when you need fast results without installing software or using complex tools.
When to use
- Quick checks or one-time calculations
- Validating or converting data before using it elsewhere
- Simple tasks that do not require advanced software
When not to use
- Critical financial, legal, or medical decisions
- Large-scale or automated processing
- Situations requiring guaranteed precision beyond basic validation
Always review results before using them in important contexts.
About this tool
This tool helps you perform quick utility operations directly in your browser. It runs entirely in your browser without sending data to a server.
You can use this tool when handling simple tasks without installing additional software. The results should be interpreted as a processed output based on your input data.
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.