why is it so hard for me to see that e^ln(x)=x?

Question

i feel stupid around my teacher when i asked this...then two weeks ago it hit me that it is obvious....but now i forgot again and can't see it. Can anyone offer an explanation that will clear up my confusion in a way where i will remember it?

Answer 1

if ln(x)=y, then by the definition of ln, x=e^y
e^(ln(x)) for ln(x)=y is e^y
so e^ln(x)=e^y which we already showed =x which is what we wanted to show. Hope this helps. If not, email me.

Answer 2

Shinu is correct! Here's a tip, always apply a function on both sides of an equation. Hope that you remember this and finally clear up the confusion.

Answer 3

take ln of both side
lne^ln(x)=lnx
lnxlne=lnx
(here lne=log(base e) e which mean =1)
lnx=lnx
hence proved

Answer 4

ln(x) = ?
I usually think to myself: "e to what power gives x?"
Now e^(lnx) = x
Remember that ln(x) means "e to what power gives x?"
Well, now you take e to that power, so obviously you get x.

Answer 5

WOA DAMNNN! I CANT DO DAT IM ONLY IN 7TH GRADE damn is this wut u olda ppl do?