Simplifying the exponential expression e^(-4 ln x +8 ln y +2)

Celeste Barajas

Celeste Barajas

Answered question

2022-11-03

Simplifying the exponential expression e 4 ln x + 8 ln y + 2

Answer & Explanation

okuzala3ul

okuzala3ul

Beginner2022-11-04Added 14 answers

e 4 ln ( x ) + 8 ln ( y ) + 2 = e 4 ln x e 8 ln y e 2 = e 2 ( e ln y ) 8 ( e ln x ) 4 = e 2 y 8 x 4
Kareem Mejia

Kareem Mejia

Beginner2022-11-05Added 9 answers

We may simplify this to
(1) f ( x , y ) = e 4 log | x | + 8 log | y | + 2 = e 8 log | y | e 2 e 4 log | x | = e log | y 8 | e 2 e log | x 4 | = e 2 y 8 x 4 ,
but notice that I, by default, use log | x | to be the same as log e | x | (or " ln") instead of log 10 | x | . Whenever you're attempting to solve or simplify things like this your first goal should be to try and get rid of the exponents. In this case it was nice because the exponents could be split up and all had a common base of e. Whatever the common base is, you use a log of that base to cancel them and be left with what is in their exponents.

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