Logarithm Calculator
Calculate logarithms, natural logs (ln), and antilogarithms with different bases. Enter your values and select the calculation type.
About Logarithms
Logarithms are the inverse operation of exponentiation. They answer the question: “To what power must the base be raised to get this number?”
Key Logarithm Concepts
- Common Logarithm (log₁₀): Base 10, frequently used in science and engineering
- Natural Logarithm (ln): Base e (≈2.71828), important in mathematics and physics
- Antilogarithm: The inverse of a logarithm, calculates aˣ
- Change of Base: Converts logₐx to logₖx using the formula logₐx = logₖx / logₖa
Logarithm Properties
| Property | Formula |
|---|---|
| Product Rule | logₐ(xy) = logₐx + logₐy |
| Quotient Rule | logₐ(x/y) = logₐx – logₐy |
| Power Rule | logₐ(xⁿ) = n·logₐx |
| Change of Base | logₐx = logₖx / logₖa |
| Natural Log | ln(x) = logₑx |
Common Applications
- Solving exponential equations
- Measuring earthquake intensity (Richter scale)
- Sound intensity (decibel scale)
- Algorithm complexity analysis
- Compound interest calculations