Natural log or natural logarithm is the logarithm with base value **e**, which is given as 2.718. Natural log is represented as log_{e} or ln. Basically there are some rules related to the natural rule like product rule, quotient rule and power rule. The formula for natural log is given as,

Related Calculators | |

Calculator Natural Log | Calculating Log |

Log10 Calculator | ph log calculator |

Let us discuss some examples of natural log.

### Solved Examples

**Question 1: **Given that ln (3) = 1.098 and ln (5) = 1.609, by using this value calculate ln (15)?

** Solution: **

Given values are,

ln (3) = 1.098 and ln (5) = 1.609, ln (15) =?

By applying product rule; ln(15) = ln ( 3 $\times$ 5 )

ln ( 3 $\times$ 5 ) = ln (3) + ln (5) = 1.098 + 1.609 = 2.707

**Question 2: **Solve ln ( $2^{5}$ ) ?

** Solution: **

Given function is ln ( $2^{5}$ )

From the power rule, this can be written as,

ln ( $2^{5}$ ) = 5 ln (2)

= 5 $\times$ 0.693 = 3.465

Given values are,

ln (3) = 1.098 and ln (5) = 1.609, ln (15) =?

By applying product rule; ln(15) = ln ( 3 $\times$ 5 )

ln ( 3 $\times$ 5 ) = ln (3) + ln (5) = 1.098 + 1.609 = 2.707

Given function is ln ( $2^{5}$ )

From the power rule, this can be written as,

ln ( $2^{5}$ ) = 5 ln (2)

= 5 $\times$ 0.693 = 3.465