Logarithm Calculator | Natural, Common, and Custom Base Logs
Calculate logarithms with different bases including natural log (ln), common log (log10), binary log (log2), and custom base logarithms with our free online calculator.
Category: Math
Logarithm Calculator
Calculate logarithms with different bases
Frequently Asked Questions
What is a logarithm?
A logarithm is the inverse operation to exponentiation. It answers the question: to what power must a given base be raised to yield a given number? For example, log₁₀(100) = 2 means 10² = 100.
What's the difference between natural log (ln) and common log (log₁₀)?
Natural logarithm (ln) uses the mathematical constant e (approximately 2.71828) as its base and is especially useful in calculus and mathematical analysis. Common logarithm (log₁₀) uses base 10 and is frequently used in engineering, physics, and everyday calculations.
How do I convert between different logarithm bases?
You can convert a logarithm from one base to another using the change of base formula: log_b(x) = log_c(x) / log_c(b), where b is the desired base and c is any other base. For example, log₂(8) = log₁₀(8) / log₁₀(2).
What are common applications of logarithms?
Logarithms are used in many fields: in science for measuring quantities like pH, decibels, and earthquake magnitude; in finance for compound interest; in computer science for algorithm complexity analysis; in statistics for data transformations; and in music theory for describing intervals between notes.