Base 10
\(\log_{10}(100) = 2\) ⇔ \(10^2 = 100\)
Logarithm Calculator
Calculate logarithms in any base with the change-of-base formula
Results
Enter values and click Calculate to see the result.
Theory & Formula
A logarithm answers the question: "To what power must we raise the base to get this number?"
If bʸ = x, then log_b(x) = y
- Common log: log₁₀(x) (base 10)
- Natural log: ln(x) = log_e(x) (base e ≈ 2.71828)
- Binary log: log₂(x) (base 2, used in computer science)
- Domain: x must be positive (x > 0)
- Change of base: log_b(x) = log_c(x) / log_c(b)
\(\log_a(x) = \frac{\ln(x)}{\ln(a)}\)
Worked Examples
Base 2
\(\log_2(8) = 3\) ⇔ \(2^3 = 8\)
Natural Log
\(\ln(e^2) = 2\) ⇔ \(e^2 = e^2\)