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Logarithms formulas
12 formulas for Logarithms, from the Algebra section of the Quantix formula library. Tap 🧮 next to a formula to solve it for any variable with step-by-step working.
| Name | Formula | Note |
|---|---|---|
| Definition | logₐ x = y ⇔ aʸ = x | a > 0, a ≠ 1, x > 0 |
| Product rule | logₐ(mn) = logₐ m + logₐ n | |
| Quotient rule | logₐ(m/n) = logₐ m − logₐ n | |
| Power rule | logₐ(mⁿ) = n · logₐ m | |
| Change of base | logₐ x = log_b x / log_b a | |
| Reciprocal | logₐ b = 1 / log_b a | |
| Base power | log_(aⁿ) x = (1/n) logₐ x | |
| Inverse | a^(logₐ x) = x | |
| Special values | logₐ 1 = 0; logₐ a = 1 | |
| Chain | logₐ b · log_b c = logₐ c | |
| Natural log | ln x = logₑ x; e ≈ 2.71828 | |
| Common log values | log 2 ≈ 0.3010, log 3 ≈ 0.4771, log 5 ≈ 0.6990 | base 10 |
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