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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 baseĀ ' e ', where ' e ' is an irrational constant that is approximately equal to 2.7182818.

 

Steps for Calculating Natural Log

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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

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  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)



    Answer  :  

    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.



    Answer  :  

    - 1.8006.



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