# Solve problem with the lambert W function?

**URL:** <https://community.wolfram.com/t/solve-problem-with-the-lambert-w-function/12127>\
**Category:** Questions\
**Tags:** calculus\
**Created:** [March 15, 2018, 2:13pm UTC](https://community.wolfram.com/t/solve-problem-with-the-lambert-w-function/12127 "2018-03-15T14:13:52Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![sadiaharoonstat](https://avatars.discourse-cdn.com/v4/letter/s/47e85d/32.png) [@sadiaharoonstat](https://community.wolfram.com/u/sadiaharoonstat)\
**Post date:** [March 15, 2018, 2:13pm UTC](https://community.wolfram.com/t/solve-problem-with-the-lambert-w-function/12127/1 "2018-03-15T14:13:52Z")

</div>

I have facing a problem in solving the lambert W function in mathematica. I have generated the x values from lambert function but I cant get the solution .ProductLog",

```
\[Phi] = 0.5; \[Kappa] = 0.2; u = RandomReal[{0, 1}, 10]; 
x = (1/\[Phi])*
   Log[(\[Kappa] - 1 + ((1 + \[Kappa])^2 - 4*\[Kappa]*u)^0.5)/(
    2*\[Kappa])] - (1/\[Phi]^2) - (1/\[Phi])*\!\(\*
ButtonBox["ProductLog",
BaseStyle->"Link",
ButtonData->"paclet:ref/ProductLog"]\)[-(1/\[Phi])*
     Exp[-(1/\[Phi])] ((\[Kappa] - 
       1 + ((1 + \[Kappa])^2 - 4*\[Kappa]*u)^0.5)/(2*\[Kappa]))]

```

---

<div class="post-metadata">

**Author:** ![danl](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/danl/32/41267_2.png) [@danl](https://community.wolfram.com/u/danl)\
**Post date:** [March 15, 2018, 3:22pm UTC](https://community.wolfram.com/t/solve-problem-with-the-lambert-w-function/12127/2 "2018-03-15T15:22:17Z")

</div>

This is not comprehensible (and the subject title is meaningless). What exactly is wanted? Something like this?

```
In[27]:= phi = 0.5; kap = 0.2; u = 
 RandomReal[{0, 1}, 
  10]; x = (1/phi)*
   Log[(kap - 1 + ((1 + kap)^2 - 4 kap u)^0.5)/(2 kap)] - (1/
    phi^2) - (1/phi)

Out[27]= {-7.50006616149, -6.17473673094, -9.36459249618, \
-8.78032746892, -9.33316651726, -9.80992590354, -6.29708140172, \
-6.01196696005, -6.34504903014, -6.70520204079}

In[28]:= ProductLog[(1/phi)*
  Exp[-(1/phi)] ((kap - 1 + ((1 + kap)^2 - 4 kap u)^0.5)/(2*kap))]

Out[28]= {0.114068677509, 0.202549549343, 0.0479727646523, \
0.063273418175, 0.0486972217016, 0.0387521917698, 0.192462165763, \
0.216647476984, 0.188623734815, 0.161819558864}

```