Quote:
 Originally Posted by hivizman ... so the equation becomes: log(-1) + log(9/4) + log(-1) + log(1/4) = 2log(3/4) Choosing values of log(-1) that cancel out (e.g. +iπ for the first log(-1) term and -iπ for the second log(-1) term), this reduces to log(9/4) + log(1/4) = 2log(3/4), which is equivalent to 9/4 x 1/4 = 9/16 = (3/4)^2 Numerically, we have: 0.3522 - 0.6020 = -0.2498 = 2 x -0.1249
Everything you did up to here is fine, but you can't possibly "choose values of log(-1) that cancel out", since you would then be using two different definitions of log in the same equation! As you said, log is not a single-valued function over the complex numbers, so then you have to choose a consistent definition of log for your means.

Of course you got values 9/4, 1/4 and (3/4)^2 which worked out in your final equation, but there is no x that would give these 3 figures.

The point then, once you get x=-5/4, you check to see if this is a valid answer, as this is the only possibility from our first equation above. It is not a valid answer, because log is not defined for -(1/4) and -(9/4) so there is no solution for x.