2xLnx-x=0

I need help solving this

  x ∈ {0, √e}

Step-by-step explanation:

Factoring the equation gives ...

  x(2ln(x) -1) = 0

This has two solutions, the values of x that make the factors be zero.

  x = 0

__

  2ln(x) -1 = 0

  ln(x) = 1/2 . . . . . . add 1, divide by 2

  x = e^(1/2) ≈ 1.64872

_____

The "zero product rule" is a very powerful aid to solving many equations. While a general polynomial involving terms with logs or exponentials cannot be solved algebraically, sometimes it can be factored in a way that admits solution—as here.

I like a graphing calculator for finding solutions to equations like this.

i need the options

step-by-step explanation:

72 is the answer to this problem