Logarithm Calculator
Calculate logarithms with any base — base 10, base e (natural log), base 2, or custom base. Shows formula, explanation and logarithm laws.
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Verification (base^result)
All Bases Side by Side
Logarithm Laws
Frequently Asked Questions
What is a logarithm?
A logarithm answers the question: to what power must a base be raised to produce a given number? If log₁₀(100) = 2, it means 10² = 100. The notation logₐ(x) = y means aʸ = x.
What is the difference between log and ln?
log (common logarithm) uses base 10. ln (natural logarithm) uses base e ≈ 2.71828. The natural logarithm appears frequently in calculus, finance (compound interest), and science. The common logarithm is used in engineering, pH calculations, and decibel scales.
What is log base 2?
Log base 2 (log₂) is used extensively in computer science because computers use binary (base 2). log₂(8) = 3 because 2³ = 8. It tells you how many binary digits (bits) are needed to represent a number.
What are logarithm laws?
Product rule: logₐ(xy) = logₐ(x) + logₐ(y). Quotient rule: logₐ(x/y) = logₐ(x) − logₐ(y). Power rule: logₐ(xⁿ) = n × logₐ(x). Change of base: logₐ(x) = log(x) / log(a).
How do logarithms relate to WAEC/JAMB exams?
Logarithms are a standard topic in WAEC Additional Mathematics and JAMB. Exam questions often test the laws of logarithms, change of base, and solving logarithmic equations. Understanding the relationship between logs and exponentials is essential.