What logarithms are and why they matter
A logarithm answers the question: 'what power do I raise the base to get this number?' log₂(8) = 3 means 2³ = 8. The logarithm is the inverse operation of exponentiation. Common logarithm (log₁₀): Base 10, written as 'log'. Used in pH (acidity), Richter scale (earthquakes), and decibels (sound). log(1000) = 3 because 10³ = 1000. Natural logarithm (ln): Base e (≈ 2.718). Used extensively in calculus, finance (compound interest), population growth, and radioactive decay. ln(e) = 1. Logarithm rules: log(ab) = log(a) + log(b). log(a/b) = log(a) - log(b). log(aⁿ) = n·log(a). Change of base: logₐ(x) = log(x)/log(a). Why logarithms matter: They compress very large ranges into manageable scales. The difference between magnitude 6 and 7 earthquakes isn't 1 unit — it's 10x more energy. Log scales make such comparisons intuitive.
Common questions about logarithms
A logarithm is the inverse operation of exponentiation. log₁₀(100) = 2 because 10² = 100.
Other useful tools related to mathematical calculations
How to Use? Enter the number and base for logarithm calculation. Use e (2.718...) for ln, 10 for log, and 2 for log2.
Logarithm with base e. ln(e) = 1, ln(1) = 0
Common logarithm with base 10. log₁₀(100) = 2, log₁₀(1000) = 3
Binary logarithm used in computer science. log₂(8) = 3, log₂(1024) = 10
Calculate logarithms with any base. log₅(125) = 3, log₃(81) = 4
Common questions about logarithms
A logarithm is the inverse operation of exponentiation. log₁₀(100) = 2 because 10² = 100.