00:01
All right, we are on question 302, and we've got 2 times e to the 6x is equal to 13.
00:10
First thing i'm going to do is i'm just going to get this a little more simplified.
00:15
I've got to start solving for x, so i'm going to divide both sides by 2.
00:20
2 divided by 2 is 1.
00:21
So we're left with e to the 6x is equal to, and i'm just going to leave this as 13 divided by 2 for now.
00:33
Okay, at this point, it kind of looks like we're stuck.
00:38
How do i get this e to go away? how do i get the exponents to be set equal to each other? how can i get the base to be the same? but if we remember that, e to the x and then our natural log, our inverses of each other, we can actually use that to get this exponent down into our base.
00:59
So over here in desmos, i actually have e to x graph because i want to show you that ln of x, they're inverse graphs of each other.
01:11
You can see they have the same shape.
01:13
They have the same kind of look to them, but they're opposite of each other.
01:21
So when we use that to our advantage, what's going to happen is our ln, our natural log, and our e are going to actually cancel each other.
01:29
Out.
01:30
So if i were to take the natural log of e v...