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Natural Logarithm

on . Posted in Algebra

Natural logarithm, abbreviated as ln, also called natural log, of a number is its logrithm to the base of the mathematical constant e (Euler number).

 

Natural Logarithm Rules

Power rule

  • \(\large{ ln \left( x^y \right) = y \left[ ln \left( x \right) \right] }\)

product rule

  • \(\large{ ln \left( x \right)\left( x \right) = ln \left( x \right) + ln \left( y \right)  }\)

Quotient rule

  • \(\large{ ln \left( \frac{x}{y} \right) = ln \left( x \right) - ln \left( y \right)  }\)

Reciprocal rule

  • \(\large{ ln \left( \frac{1}{x} \right) = ln \left( x \right)  }\)

 

Natural Logarithm Properties

  • For between 0 and 1
    • As x nears 0, it heads to infinity
    • As x increases it heads to - infinity
    • It is a strictly decreasing function
    • It has a vertical asymptote along the y-axis (x=0)
     
  • For a above 1
    • As x nears 0, it heads to - infinity
    • As x increases it heads to infinity
    • It is a strictly decreasing function
    • It has a vertical asymptote along the y-axis (x=0)