Question

Can someone help me with this one? It should be quick.

Answer 1

e^x=x^10
solve for x

I've taken the log of both sides and eventually end up with x=10lnx but can't recall how to get past that. Maybe I'm going in the wrong direction? The question basically asks to find the point of interception between the two curves.

Answer 2

@eliassaab any ideas?

Answer 3

Wolfram gives approximate answers. If wolfram can't solve it there's no way you should be able to.
http://www.wolframalpha.com/input/?i=e%5Ex%3Dx%5E10

Answer 4

I saw that on WA already. WA doesn't show how that was derived though. That's what I'm curious about.

Answer 5

Ah ok...

Answer 6

And this question is in...a text book?

Answer 7

yes... a textbook that hasn't arrived yet

Answer 8

Do you do calculus?

Answer 9

yes, it's actually in my calculus course but the root of the problem seemed more related to algebra.

Answer 10

Well ok. Have you learnt to approximate solutions?

Answer 11

drawing a blank. Again, how do I isolate "x" in x=10lnx? I'm not asking for the answer as much as asking for help getting this one concept because my brain feels like it's about to explode.

Answer 12

Oh. Sad to say, I don't think us as humans have found a way.

Answer 13

Bugs me too

Answer 14

ok, so it's not just me then... :)

Answer 15

Nup

Answer 16

Speaking of guys...do you think it's possible and we just haven't found a way, or do you think it will forever be impossible?

Answer 17

LOL... that question seems like it belongs in the philosophical section. :)

Answer 18

Haha yeah!

Answer 19

Thanks for your time!

Answer 20

Sure thing.

Answer 21

This has to be done numerically. This what I got
\[
\{\{x= -0.912765\},\{x= 1.11833\},\{x= 35.7715\}\}
\]
I used Mathematica and I got three roots.

Answer 22

Thanks!