Logarithm Calculator
Calculate log base 10, natural log (ln), log base 2, or any custom base logarithm. Instant results for all common log functions.
Logarithm Result
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Natural Log (ln) —
Log Base 10 —
Log Base 2 —
How to Use This Calculator
Enter a positive Number and select the Log Base (10, e, 2, or custom). If you choose Custom Base, enter the base value. The calculator shows the result for your chosen base plus log₁₀, ln, and log₂ all at once.
Formula
log_b(x) = ln(x) / ln(b) • log(1000) = 3 • ln(e²) = 2
Example
log₁₀(1000) = 3, ln(e) = 1, log₂(8) = 3, log₃(81) = 4
Frequently Asked Questions
- log_b(x) = y means bʸ = x. The logarithm answers: "What power must the base be raised to in order to get x?"
- The natural logarithm uses base e (≈2.71828). ln(x) = log_e(x). It appears frequently in calculus and growth formulas.
- log₂(x) tells you how many times you must multiply 2 to reach x. It is widely used in computer science and information theory.
- log_b(x) = ln(x) / ln(b) = log(x) / log(b). This lets you compute any base using natural log or log base 10.
- The number must be positive (x > 0). The custom base must be positive and not equal to 1.