The one thing about evaluating log6 14 is that it can be solved in different ways. I am trying to give you the easiest way for solving this problem.
log6 14 = ln(14)/ln(6)
= 1.146/0.778
= 1.47
From the above deduction, it can be easily concluded that the correct option among all the options that are given in the question is the first option. I hope that this is the answer that has actually come to your great help.