Natural Logarithm

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)