🔢 Math Calculator

📐 How It Works

Computes logarithms for any base. logₐ(x) asks: "to what power must a be raised to produce x?" It is the inverse of exponentiation.

🔢 Worked Examples

• log₂(8) = 3
• log₁₀(1000) = 3
• log₅(625) = 4
• log₃(81) = 4
• logₐ(1) = 0 for any a

📋 Common Use Cases

• Measuring earthquake magnitude (Richter: log₁₀)
• Sound decibels — dB = 10×log₁₀(I/I₀)
• Computer science — binary search: O(log₂n)
• Chemistry — pH = −log₁₀[H⁺]

💡 Did You Know?

Before calculators, logarithm tables (published 1614 by John Napier) allowed astronomers to multiply large numbers by looking up and adding logarithms — transforming multiplication into addition.

⚠️ Common Mistake

log(a×b) = log(a) + log(b) — NOT log(a) × log(b). Logarithm converts multiplication into addition, not into another multiplication.