Log & Antilog Calculator
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What is a Logarithm?
A logarithm answers the question: “To what power must we raise the base to get a certain number?”
If by = x, then logb(x) = y. For example, log10(100) = 2 because 10² = 100.
Common Bases
- Base 10 (common log): log10(x) – widely used in science and engineering.
- Base e (natural log): ln(x) – fundamental in calculus and growth models (e ≈ 2.718).
- Base 2: log2(x) – essential in computer science and information theory.
Useful Logarithm Properties
| Property | Formula |
|---|---|
| Product | logb(MN) = logbM + logbN |
| Quotient | logb(M/N) = logbM – logbN |
| Power | logb(Mk) = k · logbM |
| Change of base | logbx = logkx / logkb |
| Identity | logbb = 1 and logb1 = 0 |
Examples Using the Calculator
- log2 8 = ? → Base = 2, Argument = 8 → result = 3 (since 2³ = 8)
- Antilog: Base = 3, log value = 4 → result = 3⁴ = 81
- Natural log: Use base = 2.718 (e) to compute ln(x).
Why This Log Calculator Helps
Whether you’re solving exponential equations, analyzing algorithm complexity, or working with pH values, our tool gives you instant, accurate answers for any base. No more manual interpolation or complex tables!
