数学

Logarithm Calculator

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是什么 Logarithm Calculator?

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A logarithm calculator computes log base 10, natural log (ln), log base 2, and any other base. Logarithms are the inverse of exponentiation.

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公式

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f(x)log_b(x) = y means b^y = x; Change of base: log_b(x) = log_10(x) / log_10(b)

变量说明

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符号	名称	单位	描述
x	Number	—	—
b	Base	—	Usually 10, e, or 2
y	Logarithm result	—	—

如何 Logarithm Calculator

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1logₐ(x) = y means aʸ = x
2log₁₀(x): common logarithm
3ln(x): natural log, base e ≈ 2.71828
4Change of base: logₐ(x) = ln(x)/ln(a)

例题解析

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示例 1

已知:log₁₀(1000)

结果:3 (because 10³ = 1000)

示例 2

已知:ln(e²)

结果:2

实际应用

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Scientific and engineering calculations

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Earthquake magnitude (Richter scale)

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Sound intensity (decibels)

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pH calculations in chemistry

Logarithm Properties

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Property	Formula
Product rule	log(ab) = log(a) + log(b)
Quotient rule	log(a/b) = log(a) − log(b)
Power rule	log(aⁿ) = n×log(a)
Change of base	logₐ(x) = log(x)/log(a)
log(1)	Always = 0, any base

常见问题

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What's the difference between log, ln, and log₁₀?

log (no base) = log₁₀. ln = natural log (base e ≈ 2.718). log₂ = binary logarithm.

When do I use logarithms?

Solving exponential equations, measuring scales (pH, Richter, decibels), growth/decay rates.

Why is log₁₀ of 1000 equal to 3?

10³ = 1000, so log₁₀(1000) = 3. Logarithm is the inverse of exponentiation.

参考资料

›Logarithms — Khan Academy

比较

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Logarithms vs Exponents

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Reviewed October 2026

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