00:03
To combine this into a single logarithm, we're going to use all of these log properties, and we're going to start with the power property.
00:10
So if we have a number in the front, we can bring it up and make it a power.
00:12
So the one -half, we can bring that up and make it a power on x, and the five becomes a power on y, and the two becomes a power on x.
00:23
Okay, so now we have log base a of x to the one -half power, plus log -base a of y to the fifth power, minus log -base a, of x to the second power.
00:40
Okay, now according to the product rule, if you have a log plus a log, you can change it into the log of the product.
00:48
So the first two logs are added, so we can change this into log base a of x to the one half times y to the fifth.
00:57
And we still have the third logarithm there, minus log base a of x squared.
01:02
Now according to the quotient rule of logarithms, if you have a log minus a log, you can change that into the log of the quotient...