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