Natural Logarithm Rules & 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)

ln(28) = 8 ∙ ln(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

 
 
Ln of one

ln(1) = 0

  
Ln of infinity

lim ln(x) = ∞ , when x→∞

  

 

Derivative of natural logarithm (ln) function

The derivative of the natural logarithm function is the reciprocal function.

When

f (x) = ln(x)

The derivative of f(x) is:

f ' (x) = 1 / x

 

Integral of natural logarithm (ln) function

The integral of the natural logarithm function is given by:

When

f (x) = ln(x)

The integral of f(x) is:

∫ f (x)dx = ∫ ln(x)dx = x ∙ (ln(x) - 1) + C

 

Natural logarithm calculator ►

 

See also

NATURAL LOGARITHM
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