Using the Log Calculator
Both the number and base must be positive, and the base cannot equal one. Bases between zero and one are allowed, but their logarithms move in the opposite direction from bases greater than one.
Worked example
Use the example inputs below to reproduce this result. These are the form's starting values, not recommended targets. Changing your inputs updates your result above; this worked example stays fixed for comparison. Results are rounded for display.
Example inputs
- Number
- 100
- Base
- 10
Example result
- Logarithm
- 2
Method and assumptions
log base b of x = ln(x) / ln(b).
Check signs and valid inputs
Powers, roots and logarithms have restrictions that ordinary addition does not. Zero, a negative base or a fractional exponent may change whether a real-number answer exists. Read the method's supported domain and keep parentheses around negative values where the input is an expression. A rejected input may indicate a mathematical restriction rather than a formatting problem.
Common question
Why is base one not allowed?
Every power of one equals one. That cannot uniquely describe arbitrary positive numbers, so it does not define a usable logarithm base.
Guide updated .