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log

Represents the logarithmic function in mathematical expressions, typically using base 10 by default.

Overview

Essential in mathematical notation for expressing exponential relationships and solving equations involving exponential growth or decay.

  • Commonly used in computer science for analyzing algorithm complexity
  • Fundamental in engineering for describing signal processing and decibel calculations
  • Appears frequently in chemistry for pH calculations and reaction kinetics
  • Can be modified with subscripts to indicate different bases (e.g., natural logarithm, binary logarithm)
  • Particularly useful in simplifying multiplication into addition through logarithmic properties

Examples

Natural logarithm in a basic equation

y=log⁡xy = \log x 
y = \log x

Logarithm with explicit base in an equation

log⁡28=3\log_2 8 = 3 
\log_2 8 = 3

Logarithm in a more complex mathematical expression

log⁡(x2+1)=2log⁡x+log⁡(x+1x)\log(x^2 + 1) = 2\log x + \log(x + \frac{1}{x}) 
\log(x^2 + 1) = 2\log x + \log(x + \frac{1}{x})