00:02
So we're given the function for the ph, so we'll say f of x, in terms of the hydrogen ion concentration.
00:12
That's our x.
00:14
And we're tasked with determining what is the ph when the hydrogen ion concentration is 0 .1.
00:22
So that's going to equal to negative common log, right, log base 10 of 0 .1.
00:29
And with a little help from our calculator, if you want, we get that the answer is positive 1.
00:37
That makes sense because it's log base 10.
00:40
We're also then asked to determine.
00:42
So what happens if our concentration is 0 .01 and we do the same exercise, only this time we substitute in a 0 .01.
00:53
And we get that that equals 2.
00:55
We should probably go ahead and highlight these so we don't lose track.
01:00
Then we're asked, okay, let's lower it even more and find out what's the ph when our ion concentration is 0 .01.
01:16
There we go.
01:17
And that turns out to be three.
01:21
So we can see that as x decreases, f of x increases.
01:33
Right.
01:34
So ion concentration goes down is what that's telling us, concentration as it goes down, ph increases.
01:54
All right.
01:54
So next we're asked, okay, so what is the concentration if the ph, if the ph equals 3 .5, what is the hydrogen ion concentration? so to solve this, we're going to want to find the inverse function.
02:17
So we can do that.
02:21
Since we have two of these, we might as well solve first and then we'll substitute the two different numbers in...