Logarithm and Anti-Logarithm Operations

in this section. We'll take a look at the calculations involved in logarithms as well as anti log functions. Now we're going to say jen, can we learn that ph just represented the negative log of the concentration of our hydro knee um ion which could be written as H 30 plus or H plus. Now eventually we'll get to that portion again when we're talking about determining the ph of acidic and basic solutions but realize here we're gonna be introduced to logarithms right now before we even get to acids and bases. Now we're gonna say when dealing with a number with a decimal point, like the one that we have below of 12.5 we're gonna say the portion to the left of the decimal point which is right here we refer to that as the characteristic and they're gonna say the portion to the right of the decimal point. This portion here this was referred to as our man tisa. Knowing that will be incredibly important. When we take a look at log functions as well as anti log functions we're gonna say when taking the log of a number, the number of digits in the Montes of your answer is equal to the number of significant figures in the problem. Knowing this, look to see if you can answer the example that's right below where I'm giving you the log of different values and from that determine what the final answer will be. Try and attempt this on your own if you get stuck, don't worry. Just click over to the next video, you'll see how I approach those two examples that are found in example one, so give it a try and then come back and see how I do it.

So here we need to provide the answer with the correct number of significant figures for each of the following. Alright so going back to what it says here, it says the number of digits in the monte psa of your answer is equal to the number of significant figures in the problem? If we take a look here at the first one we have log of 1.15 times 10 to the negative five. We're gonna say here that our value has three sig figs in it. So there are three sig figs in the problem. Therefore the number of digits in the man tisa also has to be three. So that's how it works. So if you take your calculator typing log of this number you'll get back negative 4.9393. But we want our answer to have three digits in the man Tisa. So that's the portion after our decimal point. So the correct answer would be negative 4.939. So that would be our answer at the end for the next one. We have a log of 100 here we have a decimal point. So remember we're going this way our first non zero number is this one. And if you count all the way through we also have three sig figs there. So that means our answer. Once we find the log of this number must have three digits after the decimal point. So if you plug that in you'll get 2.0 as your correct answer. Remember when taking the log of a number the number of six figures in that number is equal to the number of digits in your man tisa. Alright, now that we've done that, let's look to see if we can do the anti logarithms portion you're gonna say here um when we're dealing with anti logarithms we're gonna say the anti log of a number X. Is equal to 10 to the X. And we're gonna say when taking the anti log of a number, we're gonna say the number of significant figures in the answer is equal to the number of significant figures in the monte psa of the problem. Okay so think of this working in the opposite direction. So look at how many digits you have in the Montes a of the problem being asked. That will help you determine the number of significant figures you'll have in your answer. So give this a try if you get stuck, don't worry, just come back we'll take a look at it together and see how we get to the answers. So good luck guys

So here it says provide the answer with the correct number of significant figures for each of the following. So let's re read what it's set up above it said here when taking the anti log of a number. The number of significant figures in the answer is equal to the number of digits in the Montes of the problem. Remember the man tisa is the portion after the decimal point. So if we take a look here we want to take the anti log of negative 4.18 here, the mantis is the portion after the decimal point. We have two digits there in the man tisa. So that means our answer has to have two significant figures. So remember anti log really just means 10 to that number and if we punch that into our calculators will get 6.6069 times 10 to the negative five. But again remember the number of digits in our monty's a is two which means we need to have 26 figs for our final answer. So this will come out to 6.6 times 10 to the negative five as our final answer. Then here is already written in the way that we need it. It's 10 to the 100.33 here, the number of digits in the monte psa is four. So that means our answer at the end must have uh four cig fix. So when we punch it into our calculator we'll have 1.00763. But again we need 466 for the final answer that comes out to 1.007 as the final answer to this question. So just remember the terms of characteristic versus man tisa and the operations that we do, whether we're taking log of that or the anti log of this. It'll become incredibly important as we delve deeper into analytical chemistry when we start talking about other things, such as uncertainties and other types of calculations where this little bit of information will go a long way to determining the final answer Yeah.