>> Okay, so in this video, we're going to look
at how to write logarithms in expanded form.
That is, in the last video, you saw
that we wrote -- we condensed the logs.
That is, we had sums and differences of different
logs, and we all condensed them into one.
Well, here we do the exact opposite.
So I have one log, and I'm going to write it as
a sum or a difference of different logs, right?
So what that means is, first of all, I don't want
anything inside the logarithm that is multiplied
or divided, and I don't want
any exponents my log, as well.
Okay, so how do I do this?
Well, the first rule I'm going to use here
is this is of the form log of x over y,
and we know this is log x minus log y, right?
So I can write this as log of x squared, y cubed
to the base 3, minus log of z the 1/2 to base 3.
Okay, now here I can split this up, right?
So multiplication, so I can use my rule that is log
of xy equals log x plus log y. Okay, and using that,
I can write this as log x squared to the base
3 plus log y cubed to the base 3 minus log z
to the 1/2 base 3, and finally, we know
what happens with our exponents right?
We can take these exponents and
multiply them out here as coefficients,
and so we have this rule, log
of x to n is n log x, right?
So I can use that one, and I can write this as 2 log x
to the base 3 plus 3 log y to the base 3 minus 1/2 log
of z. So I can write log x squared, y cubed over z to
the 1/2 to the base 3 in expanded form this way, right?
So this would be my expanded form.
