00:04
All right, we're asked to solve the equation.
00:06
It's a logarithmic equation here.
00:08
We've got log base 2 of x plus 7 equals 3 minus log base 2 of x plus 5.
00:12
I like that they have the same base.
00:14
That's going to make this pretty simple.
00:15
First thing i'm going to do is get my logs on the same side.
00:18
So log base 2 of x plus 7, we would add both sides.
00:25
Add log base 2 of x plus 5 to both sides.
00:28
So it looked like this is equal to now positive 3.
00:32
And hopefully you know how to combine your log base 2.
00:34
If you have the same base being added, we can multiply those two things.
00:38
So it becomes log base 2 of x plus 7 times x plus 5 is equal to 3.
00:48
Okay, so one more step here before i get rid of my logs, go back into exponential form.
00:54
This becomes log base 2 of them.
00:56
I'm just going to multiply mine by my binomials together.
00:59
I get x squared plus 5x plus 7x, so that's plus 12x altogether.
01:05
And then plus 35.
01:08
And that's equal to 3.
01:10
All right.
01:11
Now what i'm going to do is change this exponential form.
01:13
So it's the base to this power equals this thing.
01:18
So that means that 2 to the 3rd is equal to x squared plus 12x plus 35.
01:27
All right.
01:28
2 to the 3rd is equal to 8.
01:33
And now to solve this quadratic function, i'm going to subtract 8 from both sides so they can get it.
01:39
Equal to 0...