# Natural Log

Written by Jerry Ratzlaff 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 Log 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 Log 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)