Equation in implicit form

Question

This is simple example:

 v = {1.48622576, 1.53444276, 1.42299438}
 v/(v + 1)
 Out[1]:= {0.597784, 0.605436, 0.587288}

In the above case expression v/(v + 1) is in explicit form. I would like to find k for v = {1.48622576, 1.53444276, 1.42299438} wherein

 Log(0.5(1-k))/Log(0.5(1+k))=v (expression in implicit form)

Answer 1

As Daniel Lichtblau said in his comment the following works:

vs = {1.48622576, 1.53444276, 1.42299438};
eq[k_] := Log[0.5 (1 - k)]/Log[0.5 (1 + k)]
ks = k /. Table[FindRoot[eq[k] == v, {k, 1/2}], {v, vs}]

{0.136539, 0.1474, 0.121702}

Then you can check if the answer is correct:

vs == eq /@ ks

True