Logarithm Calculator
Calculate logarithms with base 10, base e, base 2, or any valid custom base. Includes domain checks, exact-value detection, and step-by-step explanation.
Decimal approximation: 3
What this logarithm calculator does
English search results for logarithm calculators expect one flexible tool: choose base 10, base e, base 2, or a custom base, then calculate the exponent that produces the input value.
b is the base, x is the positive argument, and y is the logarithm value.
- Use common log for base 10.
- Use natural log for base e.
- Use binary log for base 2.
- Use custom base for any positive base except 1.
Domain and change of base
x must be positive, and b must be positive but not equal to 1.
The change-of-base rule lets the calculator evaluate any valid base.
Frequently Asked Questions
Sources and References
Calculations are based on the listed reference sources. Links open in a new tab.
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