Hello to all: I was trying to solve the following question: what is the domain of the function y = log [(4-t)^(2/3)] for Real t. Here is my reasoning: The domain of the log(x) is x>0. I would have interpreted this question in terms of the log of the cubic root of (4-t)^2. Thus, I was thinking of the domain as the solution to the following inequality: (4-t)^(2/3) > 0 The cubic root has the sign of the radicand and (4-t)^2 is positive for all t. The only restriction would be when 4-t=0 and this happens for t=4. Thus, my answer to the question is: the domain is ALL reals minus 4. Apparently this is not the case as the answer to the problem is t<4. Now, I am suspecting this is because they are rewriting the function as: y=log[(2/3)*(4-t)] for which indeed the answer would be t<4. So, I am really confused as to what is going on here. Do I always need to rewrite logarithmic functions to find their domains? Why? Please, help!!! Thanks guys!