Logarithm Calculator
Free online logarithm calculator tool.
About Logarithm Calculator
The Logarithm Calculator helps you find the logarithm of a number to any base you choose. Logarithms are the inverse operations to exponentiation. They answer the question: 'To what exponent must the base be raised, to produce this number?'
How Logarithm Calculator Works
- Step 1: Base: Enter the logarithmic base (commonly 10 for standard logs, or 'e' roughly 2.718 for natural logs).
- Step 2: Number: Enter the positive number you are evaluating.
- Step 3: Calculate: The tool uses the change-of-base formula (ln(x) / ln(base)) to accurately calculate the log for any base you provide.
Frequently Asked Questions
What is a common logarithm?
A common logarithm uses base 10. If a mathematical formula just says 'log(x)' without specifying a base, it usually implies base 10.
What is a natural logarithm (ln)?
A natural logarithm uses Euler's number 'e' (approximately 2.71828) as its base. It is heavily used in calculus, physics, and compounding interest calculations.
Can I find the log of a negative number?
No. In the real number system, the logarithm of a negative number or zero is undefined. The input number must always be strictly greater than zero.