 Now the last thing we're going to do is look at some application problems. All of these application problems will involve your calculator And it is dealing with pH. So there is a formula that says that pH is equal to negative log of the hydrogen ion concentration. The hydrogen ion concentration must be in molar units for this to be appropriate. So the first problem says to find the pH if the hydrogen ion concentration is 0.45 molars. I am simply going to plug back into the formula. So using this formula pH is equal to negative log of the hydrogen ion concentration. Well, the hydrogen ion concentration was given to us as 0.45 molars. And at this point very simple all you have to do is plug it into your calculator, and you can plug it all in at one time. So negative log of 0.45 going to two decimal places will tell us that it is approximately 0.35. So we have a pH of approximately 0.35. Just to use a useful application dealing with logarithms. Let's try one more. So it's still using the same formula. So the concentration of hydrochloric acid HCl secreted by the stomach after a meal is about 1.2 times 10 to the negative 3 molars. What is the pH of stomach acid? So again using exactly the same formula. So pH is equal to negative log, and then we're going to substitute in our concentration, which is 1.2 times 10 to the negative 3. And again, we can simply type it all in. So negative log of 1.2 times 10 raised to the negative 3. And we will end up with a pH that is approximately 2.92. So the next set of examples are going to have us going backwards. Instead of finding pH, we're going to be finding the hydrogen ion concentration. And so the formula that we can use, a very simple formula that is derived from the last formula that we use, is that the hydrogen ion concentration is simply 10 to the negative pH. So looking at the first example, find the hydrogen ion concentration if the pH is 1.1. So we're looking for the hydrogen ion concentration. Again, we're simply going to substitute in. So I'm going to bring down the 10 in the formula, and I'm going to raise it to negative of my pH, and I was given that my pH was 1.1. So I simply have to substitute or plug into my calculator 10 to the negative 1.1 and taking that to two decimal places, that will give me approximately 0.08. So the hydrogen ion concentration, 0.08 molars. For the second one, find the hydrogen ion concentration if the pH is 4.56. So this time given, this is our pH using exactly the same formula. So the hydrogen ion concentration is equal to using our formula again, 10 to the negative pH, and our pH is 4.56. Simply plugging that again into the calculator and taking it to about two decimal places, that will be approximately 2.75 times 10 to the negative fifth power written in scientific notation. So that kind of sums up logarithms and their applications.