Logarithm Calculator
Calculate logarithms in any base. Shows natural log (ln), common log (log10), and custom base.
Log10 Val
2.000000
Formule
## How Logarithms Work ### Definition **log_b(x) = y means b^y = x** The logarithm answers: "To what power must I raise the base to get this number?" ### Common Types - **log₁₀(x)**: Common logarithm (base 10) - **ln(x)**: Natural logarithm (base e ≈ 2.71828) - **log₂(x)**: Binary logarithm (base 2) ### Change of Base Formula **log_b(x) = ln(x) / ln(b)**
Exemple Résolu
Calculate the logarithms of 100.
- 01log₁₀(100) = 2 (because 10² = 100)
- 02ln(100) ≈ 4.605170
- 03log₂(100) = ln(100)/ln(2) ≈ 6.643856
Questions Fréquentes
What is a logarithm?
A logarithm is the inverse of exponentiation. log_b(x) answers the question: what power of b gives x?
What is the difference between log and ln?
log (or log₁₀) uses base 10 and is common in science and engineering. ln uses base e (≈2.718) and is the natural logarithm used in calculus.
Can you take the log of a negative number?
Not in the real number system. Logarithms are only defined for positive real numbers. The complex logarithm extends this to negative numbers.
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