Are you sure with the answer my answer comes out to be (6+ log 2) and your answer as provided is (6- log 2).
If you are not sure with your answer then I will provided my solution .
pKa can never be 5.698 as -
In case 1 [ACID] > [SALT] , hence pH will be less than pKa , according to the formula -
pH = pKa + log([Salt]/[Acid]) #BufferSolution
In case 2 [ACID] < [SALT] , hence pH will be greater than pKa , as per the same formula.
But , in here in both case pH is greater than pKa which is not possible , so answer has to be -
pKa = 6.302