# Natural Log

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)