対数計算機
底10、e、カスタム底の対数問題を解く
Logarithm Properties
calculators.log.commonLogValues
出典と方法論
log_b(x) = y means b^y = xLogarithm definition and calculation
How to Use the Log Calculator
The logarithm calculator computes logarithms with any base, including common log (base 10), natural log (ln, base e), and custom bases. Visualize the log function and explore logarithm properties interactively.
What is a Logarithm?
A logarithm answers the question: "To what power must the base be raised to get this number?"
log₁₀(100) = 2 because 10² = 100
Logarithms are the inverse of exponents.
Types of Logarithms
- Common log (log or log₁₀): Base 10, used in science and engineering
- Natural log (ln or logₑ): Base e ≈ 2.718, used in calculus and continuous growth
- Binary log (log₂): Base 2, used in computer science
Laws of Logarithms
- Product Rule: log(xy) = log(x) + log(y)
- Quotient Rule: log(x/y) = log(x) - log(y)
- Power Rule: log(xⁿ) = n × log(x)
- Change of Base: log_b(x) = log(x) / log(b)
The Antilog (Inverse)
The antilog reverses the logarithm:
- If log₁₀(x) = 2, then x = 10² = 100
- If ln(x) = 3, then x = e³ ≈ 20.09
Real-World Applications
- Earthquake magnitude: Richter scale (logarithmic)
- Sound intensity: Decibel scale
- pH levels: Acidity measurement
- Compound interest: Time to reach a goal
Related Calculators
For exponent calculations, use our exponent calculator. For scientific calculations, try our scientific calculator.
よくある質問
log (common logarithm) uses base 10 and answers "what power of 10 gives this number?" ln (natural logarithm) uses base e ≈ 2.718 and answers "what power of e gives this number?" log(100) = 2 because 10² = 100. ln(e²) = 2.
No positive base raised to any real power gives a negative result. Since logarithms are the inverse of exponentials, log of a negative is undefined in real numbers. Complex logarithms exist but involve imaginary numbers.
The logarithm of 1 is always 0, regardless of base. This is because any number raised to the power 0 equals 1: 10⁰ = 1, e⁰ = 1, 2⁰ = 1. Therefore log₁₀(1) = 0, ln(1) = 0, log₂(1) = 0.
Use the change of base formula: log_b(x) = log(x) / log(b) = ln(x) / ln(b). This lets you calculate any log using a calculator that only has log and ln. Example: log₂(8) = log(8) / log(2) = 0.903 / 0.301 = 3.
Logarithms measure things that vary by orders of magnitude. The Richter scale (earthquakes), decibel scale (sound), and pH scale (acidity) are all logarithmic. They also solve exponential growth problems, like finding how long until an investment doubles.
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