Exponents & Logarithms Solver
Solve for any variable in exponential and logarithmic equations. Includes base change steps and domain validation.
About
Exponential and logarithmic equations describe relationships where growth is proportional to current size, used heavily in finance (compound interest), physics (radioactive decay), and computer science (complexity algorithms). This tool solves for any variable in the relationship ab = c, which is mathematically equivalent to loga(c) = b.
Unlike simple calculators, this solver verifies domain constraints (e.g., logarithmic bases must be positive and non-unity) and provides step-by-step logic, including change-of-base transformations necessary for calculation on standard devices.
Formulas
The core transformation relies on the equivalence:
Solving for the exponent requires the logarithm:
Reference Data
| Identity Name | Formula | Notes |
|---|---|---|
| Definition | logb(x) = y ⇔ by = x | Inverse operations |
| Product Rule | log(xy) = log(x) + log(y) | Map mult to add |
| Quotient Rule | log(x/y) = log(x) − log(y) | Map div to sub |
| Power Rule | log(xp) = p ⋅ log(x) | Exponents move out |
| Change of Base | logb(x) = ln(x)ln(b) | Essential for calc |
| Log of 1 | logb(1) = 0 | Intercept |
| Log of Base | logb(b) = 1 | Unity |
| Natural Log | ln(e) = 1 | Base e ≈ 2.718 |