Log Calculator
Calculate logarithms, natural logs, and antilogs with step-by-step solutions
Calculator
Calculate log with a custom base.
Calculate natural log, common log, and binary log simultaneously.
Find the antilogarithm (inverse of log): by = x
Explore logarithm properties with your values.
Results
Understanding Logarithms
A logarithm answers the question: “How many of one number do we multiply to get another number?” For example, log₁₀(100) = 2 because 10 × 10 = 100, or 10² = 100.
Common Logarithm Types
- Natural Log (ln): Base e (≈ 2.71828) — used in calculus, physics, and continuous growth
- Common Log (log): Base 10 — used in science, engineering, and pH calculations
- Binary Log (lb): Base 2 — used in computer science and information theory
Key Logarithm Properties
Real-World Applications
- Science: pH scale, Richter scale for earthquakes, decibel scale for sound
- Finance: Compound interest calculations and investment growth models
- Computer Science: Algorithm complexity (Big O notation), data compression
- Engineering: Signal processing, filter design, control systems
- Medicine: Drug dosage calculations and bacterial growth rates
How to Calculate a Logarithm Using This Log Calculator
This free Log Calculator computes the logarithm of any positive number across the most commonly used bases: base 10 (common log), base e (natural log or ln), base 2 (binary log), or any custom base you enter. Enter your number, select the base, and get the result instantly. Logarithms are the inverse of exponentiation and appear across mathematics, physics, engineering, and computer science. Base 10 is standard in science and engineering, base e appears in calculus and exponential growth problems, and base 2 is used in data storage and algorithm analysis. No formula lookup, no manual calculation needed.