00:01
Suppose i wanted to simplify this into one logarithm.
00:03
First, it's to review the rules of logarithms.
00:06
Well, first thing i know is that if i'm multiplying inside the same logarithm, then i could separate them by adding with the logarithm of the same base.
00:17
I also know if i'm dividing in the same logarithm, then what i'm doing is i'm just subtracting the numerator minus the denominator, still applying the same logarithm.
00:28
And finally, if i have an exponent inside a logarithm, i could bring that exponent down in front and multiply it in front of the logarithm.
00:35
So i could use either of these three rules here.
00:38
But the first rule i want to use is i have the third root.
00:43
Okay, recall that this is raising each term to the one -third power.
00:49
So it's m to the 12th to the one -third power, and to the ninth to the one -third power over a to the four to the one -third and b, the fifth to the one -third.
00:58
And what i can do is, since this is outside, i can multiply this to each of these terms.
01:03
So this is log base a.
01:05
This will be m.
01:07
12 divided by 3 is 4, and 9 divided by 3 is 3...