Consider f (x) = logk (6x - 3x 2 ), for 0 < x < 2, where k > 0. The equation f (x) = 2 has exactly one solution. What is the value of k?

There are two essential tricks to grasp in this question. Firstly, since the equation has only one solution, the Discriminant that will be required would equal 0. Secondly, since we are given f(x) = 2 we can write it in a different form: logk k2. This will allow us to cancel the logarithms. Then it is a basic quadratic function. The result would be +- square root of 3, but given that k is larger than 0, it automatically selects the positive value only.