00:01
Let?s move on to our second rule of log.
00:03
So, our second rule of log stated if you have log base a, x over y
that is the same as log base a of x minus log base a of y.
00:15
Now, it's very similar to the first rule, we start off doing the same thing
makes substitutions for p so this can be p log base a of x
and this can be q log base a of y, you can then rewrite this in index form,
so let?s just say we're changing this to index form here,
so, that becomes a to the p equals to x and that becomes a to the q equals to y.
00:43
So, it's exactly the same step as you did with the first proof,
we're now starting our proof with trying to prove this part here,
so you can say that x over y, so this is x this is y and x is a to the p,
so you can rewrite this is a to the p over a to the q,
which if you?re dividing to base numbers you can rewrite this is a to the p minus q.
01:07
So, so far, we can say we have x over y equals to a to the p minus q,
you extend this a little bit so you log both sides,
so we're going to have log base a of this and log base a of this.
01:22
Looking back at our previous proof, you know that you can bring p minus q down
and this entire thing by itself will just equal to one,
so, we have log base a, x over y and if you replace your p and q, so, p is log base a of x
and q is log base a of y, we can write this as that minus log base a of y,
if we just write it out in one line here.
01:48
So, log base a, x over y as the same as log base a of x minus log base a of y.