1+1

f[c_] :=-(c-1) ProductLog(-1,-1/((c-1) e^(1/(c-1))))/ln(-(c-1) ProductLog(-1,-1/((c-1) e^(1/(c-1)))))

1+1

f[2]

f[3]

f[1.4]

1+1

b_val[c_] := -(c-1)* N[ProductLog[-1,-1/((c-1) e^(1/(c-1)))]]

b_val[2]

b_val[2]

b_val[2]

ProductLog[-1.4]

ProductLog[-1,1]

N[ProductLog[-1,1]]

-1.5339133197935744`-4.375185153061898` I

N[ProductLog[-1,-0.1]]

b_val[2]

b_val[2]

N[b_val[2]]

b_val[2]

acab[c_] := -(c-1)N[ProductLog[-1,-1/((c-1) Exp[1/(c-1)])]]

acab[2]

b_val[2]

f[c_] := N[acab[c]/Log[acab[c]]]

acab[1.2]

Plot[acab[c],{c,0,10}]

Plot[f[c],{c,2,10}]