In[]:=
ClearAll["`*"];Remove["`*"]
In[]:=
f[θ_]:=w*
2
Log[θ]
Log[2]
+
2L*V*
Log[θ]
Log[2]
t
2-p
In[]:=
S=Solve[f'[θ]==0,θ]//Quiet
Out[]=
θ
-
ProductLog-
LV
2
Log[t]
(-2+p)w

Log[t]
2

In[]:=
w=100000;​​L=3240000;​​V=0.0625;​​t=2;​​p=0.75;​​θ/.S[[1]],Exp-
LambertW
LV
2
Log[t]
w(2-p)
*Log[2]
Log[t]
(*TRUE*)
Out[]=
{0.618107,0.618107}