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# Natural Log Formula

Natural log or natural logarithm is the logarithm with base value e, which is given as 2.718. Natural log is represented as loge 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,

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## Natural Log Examples

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

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