Question

How to proof that this not have solution?
lnx = x => e^x = x

Answer 1

by induction

Answer 2

You talking about why sqrt(2) is irrational? Is the same idea?

Answer 3

let x be an element of R such that
choose x=-1
substitude to inx=x
in(-1)\[\neq-1\]
it implies that
e^x\[\neq x\]

this also implies that any real number does not hold to the proof by substituting .

Answer 4

prove it analytically.

Answer 5

e^x > 0 for all values of x
so when x is negative or equal to 0, e^x > x

the slope of e^x is e^x while the slope of x is 1, e^x >1 for all x > 0,
hence e^x is greater than x at 0 to begin with and increases at exponential rate. so e^x > x for all values of x. Hence there is no solution.

Answer 6

wat if x=1

Answer 7

something that begins with greater value and increases at greater rate will always be greater.

Answer 8

thanks!!