SOLUTION: Can someone please explain why logbx/ logby does not equal logbx

SOLUTION: Can someone please explain why logbx/ logby does not equal logbx - logby?

Question 274779: Can someone please explain why logbx/ logby does not equal logbx - logby?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
To prove something false, we usually resort to a counterexample. A counterexample is an explicit example in which proves a theorem or equation false (usually by a contradiction of some sort).

So let's say that and . This would then mean that

Now plug and into to get

So in short, and when and .

Clearly which means that when and .

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Here's another way of looking at it.

By the change of base formula,

By another identity,

So let's assume that . If this is the case, then

Equate the bases and arguments to get and . The second equation simplifies to . Solve for b to get .

Now if , this means that which is impossible (you can't divide by zero).

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