Logarithm Calculator
Calculate logarithms with different bases, natural logarithms, and antilogarithms. Perfect for students, scientists, and professionals working with mathematical analysis.
Logarithm Calculator
Calculate logarithms with different bases, natural logarithms, and antilogarithms
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About Logarithms
• Logarithm: log_b(x) = y means bʸ = x
• Natural Log: ln(x) = log_e(x) where e ≈ 2.71828
• Common Log: log₁₀(x) is the base-10 logarithm
• Antilogarithm: b^x is the inverse of log_b(x)
Common Logarithm Types
Logarithm Properties
Understanding Logarithms
A logarithm is the inverse operation of exponentiation. If bʸ = x, then log_b(x) = y. Logarithms are fundamental in mathematics and have numerous applications in science, engineering, and finance.
Common logarithm (log₁₀) uses base 10 and is widely used in scientific notation and pH calculations. Natural logarithm (ln)uses base e (≈ 2.71828) and appears naturally in calculus and many scientific formulas.
Logarithms have special properties that make them useful for simplifying complex calculations, especially those involving multiplication, division, and powers.
How to Use This Calculator
Logarithm Applications
Chemistry & pH
pH = -log₁₀[H⁺], where [H⁺] is the hydrogen ion concentration. Logarithms help measure acidity and alkalinity.
Data Analysis
Logarithms compress large ranges of data, making it easier to visualize and analyze exponential relationships.
Finance & Growth
Logarithms help calculate compound interest, growth rates, and time value of money calculations.