00:01
In this problem, you're being asked to solve the given equation.
00:03
So we have 3 raised to the 8x power minus 3 raised to the 4x power minus 6 equal to 0.
00:09
So what i'm going to do is i'm going to solve this equation by using substitution.
00:13
So i want this equation ultimately to look like a quadratic equation.
00:17
Now notice that our middle term is 3 raised to the 4x power.
00:21
So i'm going to let u equal to 3 raised to the 4x power.
00:26
Now let's take a look at that first term, 3 being raised to the 8x power.
00:30
Well, if i wanted to rewrite that in terms of the 4x power, it would be 3 to the 4x all raised to the second power.
00:37
Because according to our exponent rules, we would multiply these exponents.
00:40
So perfect.
00:41
So then i'll bring down minus 3 raised to the 4x power minus 6 equal to 0.
00:46
And now let's go ahead and substitute u in place of 3 to the 4x.
00:50
Well, that's going to leave us with u squared minus u minus 6 equal to 0.
00:56
And now we have a quadratic equation.
00:58
So i'm going to solve this by factor.
00:59
Well, because the first term has a coefficient of 1, i know that both of my factors are going to start with u because u times u is u squared.
01:07
So we just have to find two numbers that multiply the negative 6 that will give us negative 1.
01:12
Well, that would be negative 3 and positive 2.
01:15
So now that we have our factors, we can set them both equal to 0, meaning that u minus 3 could equal to 0 or that u plus 2 could equal to 0...