Logarithm Calculator
Calculate logarithms with any base, including natural (ln) and common (log) logarithms
Logarithm Formulas
Basic Definition
logb(x) = y means by = x
Where b is the base and x is the number
Common Types
ln(x) = loge(x) (Natural)
log(x) = log10(x) (Common)
lb(x) = log2(x) (Binary)
Properties
logb(x×y) = logb(x) + logb(y)
logb(x/y) = logb(x) - logb(y)
logb(xn) = n×logb(x)
Benefits & Features
Our logarithm calculator offers multiple advantages:
Comprehensive Calculations
- Natural logarithm (ln)
- Common logarithm (log)
- Binary logarithm (lb)
- Custom base logarithms
- Step-by-step explanations
Easy to Use
- Simple and intuitive interface
- Auto-calculation feature
- Multiple base options
- Clear result display
- Mobile-friendly design
Versatile Applications
- Scientific calculations
- Engineering problems
- Data analysis
- Information theory
- Sound and signal processing
Frequently Asked Questions
A logarithm is the inverse of exponentiation. If b^y = x, then log_b(x) = y. For example, since 10³ = 1000, log₁₀(1000) = 3. Logarithms help us solve exponential equations and are useful in many scientific applications.
ln (natural logarithm) uses base e (≈2.71828) while log (common logarithm) uses base 10. For example, ln(100) ≈ 4.605 while log(100) = 2. Both are widely used in different scientific fields.
Logarithms of negative numbers are undefined in the real number system. This is because no real number raised to any power can give a negative result. However, logarithms of negative numbers exist in complex mathematics.
Our calculator uses JavaScript's built-in Math functions for calculations, providing results with high precision (up to 6 decimal places). For very large or small numbers, results may be shown in scientific notation.