Logarithm Calculator
Evaluate Logarithms
Compute natural log ln(x), common log log10(x), and custom base log_b(x) using change of base.
Solve Log/Exponential Equations
Solve basic equations involving logarithms and exponentials: log_b(x)=y, b^x=y, and a·log_b(x)=c.
About Logarithms
Logarithms are inverses of exponentials. The natural log ln(x) uses base e, the common log log10(x) uses base 10, and logs with custom base b can be evaluated using the change-of-base formula.
Formulas
- Change of base: log_b(x) = ln(x) / ln(b)
- Definition: log_b(x) = y ⇔ b^y = x
- Properties: log_b(xy) = log_b(x) + log_b(y), log_b(x^k) = k·log_b(x)
Notes
- Domain: x > 0; base b > 0 and b ≠ 1
- Equations often reduce to exponentials or use change of base