e^(1/x) = 1/(ln x)?

Answer 1

they are not equal
easy to put the number to see
or if yoy put x= 1 the rhs will be undefined
but lhs is e.

Answer 2

Are you trying to find for what x they are equal or if they are always equal?

They are not always equal

Just try x = 1.

e^(1/1) = 1/ln(1)
e^1 = 1/0
e = Undefined

Both sides are clearly not equal. If you look at the graphs, you'll see a lot of symmetry, but they are not always overlapping.


There is an x where they are both equal: 1.7632. I'm not sure if there's an algebraic way to find that solution - I just used my graphing calculator and found the intersection.

Answer 3

I don't think so! Try a few values for x and use your calculator.