Logarithm Calculator
Calculate logarithms with different bases. Choose natural log (ln), common log (log base 10), or enter a custom base.
Logarithm Result
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Enter a number and click calculate
Quick Examples
What is a Logarithm?
A logarithm answers the question: "To what power must a base be raised to get a given number?" It is the inverse operation of exponentiation.
If b^x = y, then log_b(y) = x
Types of Logarithms
- Common Log (log₁₀): Used in engineering, pH scale, decibels
- Natural Log (ln): Base e ≈ 2.71828. Essential in calculus and physics
- Binary Log (log₂): Important in computer science and information theory
Logarithm Rules
| Rule | Formula |
|---|---|
| Product Rule | log(xy) = log(x) + log(y) |
| Quotient Rule | log(x/y) = log(x) - log(y) |
| Power Rule | log(xⁿ) = n·log(x) |
| Change of Base | log_b(x) = ln(x)/ln(b) |
Frequently Asked Questions
What is a logarithm?
A logarithm is the inverse of exponentiation. If you ask "10 to what power equals 100?", the answer is 2, so log₁₀(100) = 2.
What is the difference between log and ln?
log typically means log base 10 (common log), while ln always means natural log with base e (≈2.71828). Natural log is essential in calculus.