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Natural Log Calculator
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 Natural Log Calculator (or Natural Logarithm Calculator) is an online tool for calculating the natural logarithm of a number x, which is generally written as In(x) or loge(x). The natural logarithm is said to be the logarithm to the base ' e ', where ' e ' is an irrational constant that is approximately equal to 2.7182818.

## Steps for Calculating Natural Log

Step 1 :

Laws of Natural Logarithms

Below you could see laws which helps us to solve the problems of natural log.

Here, In x = loge x

In (e) = 1

In (x * y) = (In x) + (In y). (Product Rule)

In $(\frac{x}{y})$ = (In x) - (In y) (Quotient Rule)

In (xn) = (n) In x  (Power Rule)

Step 2 :

Apply the laws of natural log depending on the construction of the problem.

## Natural Log Calculation Problems

1. ### Natural log, ln 3 = 1.10 and ln 5 = 1.61 . Find ln 45

Step 1 :

Since 45 = (5)(32) We have

Apply the laws of natural log for (45)

We use (Product Rule) here,

In (x * y) = (In x) + (In y).

Step 2 :

ln 45 = ln (5)(32)

= ln 5 + ln 32

= 1.61 + 2 ln 3

= 1.61 + 2 (1.10)

3.81

2. ### Solving natural log of the given expression, ln(3x + 60) = 4.

Step 1 :

Given: ln(3x + 60) = 4

Conversions of the natural log to exponential form:

3x + 60 = e4

Where e = 2.7182818

Step 2 :

3x + 60 = 54.5981 [ e4 = 54.59815]

Take -60 on both sides

(3x + 60 ) - 60 = 54.5981- 60

3x = -5.4019

Divide by 3 on both sides

x = -1.8006

Therefore, by solving natural log equation we get the value of x = - 1.8006.