Logarithm Calculator
Calculate natural logarithms (ln), common logarithms (log₁₀), and logarithms with custom bases. Perfect for solving exponential equations and working with logarithmic functions.
Example Calculations
Natural Logarithms
Common Logarithms
Custom Base Logarithms
Logarithm Formulas and Properties
Basic Definitions
- logb(x) = y means by = x
- ln(x) = loge(x) (natural logarithm, base e)
- log(x) = log10(x) (common logarithm, base 10)
- logb(b) = 1 (logarithm of base to itself)
- logb(1) = 0 (logarithm of 1 to any base)
Logarithm Rules
- logb(x·y) = logb(x) + logb(y) (product rule)
- logb(x÷y) = logb(x) - logb(y) (quotient rule)
- logb(xn) = n·logb(x) (power rule)
- logb(x) = logc(x) ÷ logc(b) (change of base)
Applications of Logarithms
Mathematics
- • Solving exponential equations
- • Rate of growth/decay analysis
- • Series expansions
Science
- • pH scale in chemistry (uses -log10)
- • Richter scale for earthquakes
- • Decibels in acoustics
- • Stellar magnitude in astronomy
Other Fields
- • Information theory (log2 for bits)
- • Compound interest calculations
- • Signal processing
- • Data compression algorithms
- • Machine learning (log-likelihood)