This only functions if a is zero, undefined, or some unreal number. It isn't allowed to be anything else.
It's like √(a2)=a. If a=-1, this is untrue.
Or even better, loga c=b, where c=0. If a<1, then b must be infinite. If a>1, then b must be infinitely negative. If a=1, then b is not even a real number. These laws of mathematics have exceptions that must be left out, certain values that a variable cannot be.
Also, I guess this applies to the original problem as well, but I'm on page two, so meh effort.