Answered

Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

ln(1/e^2) without calculator

Sagot :

Everest2017
Ln 1/e²
             =  Ln 1 -  Ln e²       as  Ln X/Y = Ln X  -  Ln Y
             =  0  -  2 Ln e         as Ln 1 = 0    and  Ln X²  = 2 Ln X
                = - 2  * 1          as Ln e  = 1

        = -2


AL2006
Once you remember the definition of a log, the answer to this question will literally fall out of your pencil.

First, ' Ln ' means 'natural log' ... logs to the base of ' e '.

Definition of the natural log of a number:
In order to get the number, what power do I have to raise ' e ' to ?

OK.  What power do you have to raise ' e ' to in order to get  1/e²  ?

Isn't  1/e²  the same thing as  e⁻²  ?

So, in order to get  1/e² , you have to raise ' e ' to the  -2  power .

In math-speak:    Ln(1/e²) = -2 .
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.