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Logarithm

★★★☆☆High School

📖Definition

The inverse of exponential function, indicating how many times a base must be multiplied to get a number.

📐Formulas

logₐ b = c ⇔ a^c = b

Definition of logarithm

  • aBase (a > 0, a ≠ 1)
  • bArgument (b > 0)
  • cLogarithm value
logₐ(xy) = logₐ x + logₐ y

Product rule

logₐ(x)/(y) = logₐ x - logₐ y

Quotient rule

logₐ xⁿ = n logₐ x

Power rule

logₐ b = (log_c b)/(log_c a)

Change of base formula

✏️Examples

예제 1★★☆☆☆

Find log₂ 32.

예제 2★★☆☆☆

Calculate log₁₀ 2 + log₁₀ 5.

Applications

Science

pH scale, decibels

Computing

Algorithm complexity (O(log n))

Seismology

Richter scale

🔗Related Documents

Prerequisites

Related

#algebra#function#logarithm#advanced