Question

we have e^ln(x) = ? for each positive number x, and ln(e^x) =? for all real numbers x.

Answer 1

first one =x
second one =x

Answer 2

Both are just x. You have inverse functions. So you have:
\[f(x) \]
and
\[f^{-1}(x)\]
In the first case you have:
\[f(f^{-1}(x))\]
And in the second you have:
\[f^{-1}(f(x))=x\]

Answer 3

take e^lnx = y.. and take ln on both sides .. then take antilog ..

Answer 4

Think about x^2 and sqrt(x). If you have (sqrt(x))^2 or sqrt(x^2). Both are x.

Answer 5

ans = X in each case