logLogarithm Equation Solver
e.g. 2, e, 10
A logarithm is the inverse of exponentiation: log_b(x) = y means b^y = x. Logarithms compress large ranges of values (useful for the Richter scale, decibels, pH, information theory), linearise exponential relationships, and are central to many mathematical formulas. The natural logarithm (base e) and base-10 logarithm are the most commonly used.
- 1log_b(x) = ln(x) / ln(b) — change of base formula
- 2Natural log ln(x) = log_e(x), where e ≈ 2.71828
- 3Common log log₁₀(x) = log(x) in most contexts
- 4Binary log log₂(x) — used in information theory and computer science
- 5log_b(x) is undefined for x ≤ 0 or b ≤ 0 or b = 1
log₁₀(1000)=310³ = 1000
log₂(256)=82⁸ = 256 — bytes to bits
ln(e⁵)=5Inverse of e^x
| Law | Formula |
|---|---|
| Product | log(ab) = log(a) + log(b) |
| Quotient | log(a/b) = log(a) − log(b) |
| Power | log(aⁿ) = n·log(a) |
| Change of base | log_b(x) = ln(x)/ln(b) |
| Inverse | b^(log_b(x)) = x |
| log(1) | = 0 for any base b |
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