SOLUTION: Apologies if this has been asked before, as unregistered users cannot search the massive answer archives. I have a problem here that asks me to prove that "log base b of 0 is un

Question 954243: Apologies if this has been asked before, as unregistered users cannot search the massive answer archives.
I have a problem here that asks me to prove that "log base b of 0 is undefined". I start by saying that "log base b of 0 = x" ("x is undefined" thus being where I need to get to to prove what I've been told to prove), then go to "b^x = 0", then "x*log b = log 0", then "x=(log 0)/(log b)". There was another way I attempted to go about it, but I don't remember exactly what it was, and it took me to the same place, where my brain just sort of stalls. On the face of it, it seems patently obvious that there is no power of anything except zero that would be equal to zero, but I can't figure out what to cite to say this or any other way to move beyond here. I thought at one point of attempting to force a divide by zero on one side with x on the other, but couldn't figure out how to do that either.
There's got to be something painfully obvious I'm missing here. Help!
Matt.
Answer by josgarithmetic(39792) (Show Source): You can put this solution on YOUR website!
Only two suggestions are to assign a variable (as you did, x, or a different variable name) and GIVE that it is a real number. Other suggestion is to change from log form into exponential form. Try to work through logical pathways to show a contradiction.

Imagine three cases for the possible domain of x.
x may be any of , , .
Examine the meaning of each of those cases.
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