Mister Exam

Other calculators

x+log(x)/x=0

x+log(x)/x=0 equation

The teacher will be very surprised to see your correct solution 😉

v

Numerical solution:

Do search numerical solution at [, ]

The solution

You have entered [src] 
    log(x)    
x + ------ = 0
      x
$$x + \frac{\log{\left(x \right)}}{x} = 0$$
Simplify
The graph
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
      -W(2) 
      ------
        2   
x1 = e
$$x_{1} = e^{- \frac{W\left(2\right)}{2}}$$ 
x1 = exp(-LambertW(2)/2)
Sum and product of roots [src] 
sum
 -W(2) 
 ------
   2   
e
$$e^{- \frac{W\left(2\right)}{2}}$$ 
=
 -W(2) 
 ------
   2   
e
$$e^{- \frac{W\left(2\right)}{2}}$$ 
product
 -W(2) 
 ------
   2   
e
$$e^{- \frac{W\left(2\right)}{2}}$$ 
=
 -W(2) 
 ------
   2   
e
$$e^{- \frac{W\left(2\right)}{2}}$$ 
exp(-LambertW(2)/2)
Numerical answer [src] 
x1 = -0.971099875462555 + 1.1662719028764*i
x2 = -0.971099875462555 - 1.1662719028764*i
x2 = -0.971099875462555 - 1.1662719028764*i
The graph
x+log(x)/x=0 equation
    © Mister Exam – Calculator