>> All right.
So in this video what we're going to look at is
we're going to look at how do we condense logs.
Right, if I have a string of logs, like this,
how do I condense them into a single log?
And, again, this is very useful for us
when we start solving equations in logs.
Right? So one of the things you want to make
sure here is that you want to have only log.
All right?
All of this needs to be written inside of one log.
So how do I do that?
Well, let's see.
If you remember the rule here, the two
rules that we really used, we use here,
will be log of x plus log of y equals log xy.
Right? And then log of x minus log of y equals log x/y.
Okay? And then one more that will be useful to us
will be log of x to the n equals n log x. Right?
So basically these are the three
rules that we'll use a lot in trying--
when we try to condense logs or in the next
video we will see when we try to expand them.
Okay? So, first thing I want to do here is I
want to take care of these coefficients, right?
So what do I do with my coefficients?
If you look here, the coefficient
can become an exponent.
Right? So I can rewrite this as log 3 plus.
Now the 2 log x will become log of x squared.
And the 6 log 7 can become minus
log of 7 to the base 6.
Okay? Now that I've taken care of the coefficients,
what I can do now is I can use this property
here, so I have log x plus log y is log xy.
And so I'm going to go ahead
and I'm going to say, this is--
I can add these two by saying
this is log of 3 times x squared.
Okay? Minus log of 7 to the power 6.
Okay? So I've already condensed them
here, and now finally I have two logs
and subtracting two logs I'm going
to use this property over here,
where I have log x minus log y equals log of x/y.
And so that's going to give me log
of 3 x squared over 7 to the 6th.
And that is the condensed form of the log.
