Same Log Both Sides

In log_4(3x - 1) = log_4(x + 5) there is a log on each side, with the same base. Two logs of the same base are equal only when their insides are equal, because each output of a log comes from exactly one input. So drop the logs: 3x - 1 = x + 5, which gives x = 3.

This needs the same base on both sides: log_2(x) and log_4(x) are different functions, so their insides cannot simply be matched.

Then check, as always. With x = 3 both insides are 8, which is positive, so the answer stands. If a candidate made an inside zero or negative, that log would have no value and the candidate would be thrown out.