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1 / Natural Logarithm - ln(x) Natural logarithm is the logarithm to the base e of a number. Definition of natural logarithm When e y = x Then base e logarithm of x is ln( x ) = log e ( x ) = y The e constant or Euler's number is: e ≈ 2.71828183 Ln as inverse function of exponential function The natural logarithm function ln(x) is the inverse function of the exponential function e x . For x>0, f (f -1(x)) = eln(x) = x Or f -1(f (x)) = ln( ex Natural logarithm rules and properties Rule name Rule Example Product rule ln( x y ) = ln( x ) + ln( y ) ln(3 7) = ln(3) + ln(7) Quotient rule ln( x / y ) = ln( x ) - ln( y ) ln(3 / 7) = ln(3) - ln(7) Power rule ln( x y ) = y ln( x ) l n ( 2 8 ) = 8 l n ( 2 ) ln derivative f ( x ) = ln( x ) ⇒ f ' ( x ) = 1 / x ln integral ∫ ln( x ) dx = x (ln( x ) - 1) + C ln of negative number ln( x ) is undefined when x ≤ 0 ln of zero ln(0) is undefined
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Logarithm product rule The logarithm of the multiplication of x and y is the sum of logarithm of x and logarithm of y. log b ( x y ) = log b ( x ) + log b ( y ) For example: log 10 (3 7) = log 10 (3) + log 10 (7) Logarithm quotient rule
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  • Fall '19
  • Natural logarithm, Logarithm

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