Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have this simplification in my textbook, $$e^{-(x+3\log|x|)} = x^{-3}e^{-x}$$

I cant get how did we got that? i know this rules $e^{\log|x|}=x$ and $e^{x+y}= e^xe^y$

Are those things related? Can someone explain me this? Thanks

share|improve this question
1  
That rule should say $e^{\log|x|}=|x|$, which is equal to $x$ if $x$ is positive. Also, recall that all this assumes that "$\log$" means natural logarithm, i.e. the base is $e$. –  Michael Hardy Dec 28 '12 at 19:30
add comment

1 Answer 1

up vote 2 down vote accepted

Well $$e^{-x-3\log x}=e^{-x}e^{-3\log x}=e^{-x}(e^{\log x})^{-3}=e^{-x}x^{-3}$$ and there you have it. Note that I used that $x^{yz}=(x^y)^z$

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.