Logarithmic Equation Solver
A specialized algebra calculator for solving logarithmic equations including Natural Log (ln). Features automatic simplification of log properties and domain validity checking.
About
Logarithmic equations pose unique challenges due to domain restrictions; the arguments of logarithms must strictly be positive real numbers. This solver handles equations in the form logb(x) = y and complex combinations using the Product, Quotient, and Power rules. Accuracy is maintained by validating solutions against the original domain to filter out extraneous roots that frequently appear during algebraic manipulation.
The tool supports variable bases, including the natural base e (entered as ln). It isolates the variable x by converting the logarithmic form to exponential form x = by or by equating arguments when bases match.
Formulas
To solve equations where the variable is inside the log, convert to exponential form:
For equations with logs on both sides:
Reference Data
| Property Name | Formula Identity | Condition |
|---|---|---|
| Product Rule | logb(M×N) = logb(M) + logb(N) | M,N > 0 |
| Quotient Rule | logb(MN) = logb(M) − logb(N) | N > 0 |
| Power Rule | logb(Mp) = p ⋅ logb(M) | M > 0 |
| Change of Base | logb(M) = ln(M)ln(b) | b ≠ 1 |