Question

why e^lnf(x) = f(x), where can I FIND the proof of it?

Answer 1

e^lnf(x)=e^log(e)(f(x))=f(x)

Answer 2

that's it, is it a proof? it just flew over my head :|

Answer 3

by definition of the lgarithm\[\log_ax=y\iff x=a^y= a^{\log_a x}\]

Answer 4

ok, that right

Answer 5

no ngoc... just restated the problem and proved nothing
no offense...

Answer 6

let \[y = e^{lnf(x)}\]
taking log on both sides...
\[\ln y = \ln e^{lnf(x)}\]
since\[lnx^m = mlnx\]
so
\[lny = lnf(x)lne\]
also ln(e) = 1
so lny = lnf(x)
so y = f(x)
but \[y = e^{lnf(x)}\]
so \[f(x) = e^{lnf(x)}\]

Answer 7

ok, the same

Answer 8

it is definition

Answer 9

thanx @ savy

Answer 10

@Savvy very rigour proof

Answer 11

did you follow mine wounded tiger?
it may not be as elaborate, but I think it is solid

Answer 12

lol...your welcome dude...