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Logarithm Calculator
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Home/Math/Log
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If 10² = 100, then log₁₀(100) = 2. Logarithms "undo" exponents. They're inverse operations, like division undoes multiplication.
To calculate log₃(27) on a calculator, use: log₃(27) = ln(27) / ln(3) ≈ 3. This works for any base!
ln appears in compound interest, radioactive decay, and population growth. When something changes continuously (not in steps), you'll see e and ln.
You can't split addition! Correct rule: log(a × b) = log(a) + log(b). And log(a / b) = log(a) - log(b).
You can't take the log of a negative number or zero (in real numbers). log(-5) is undefined.
log₁(x) is undefined because 1 to any power is still 1. The base must be positive and ≠ 1.