Inverse Logarithmic Functions

Jules Bruno
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the inverse or anti log horrific function can be seen as the opposite of your logo rhythmic function. We're gonna say. Here, let's take for example, Log of X gives me why. If we take the anti log or the inverse log off, why, then that would give me 10 to the Y, which is equal to X. So what does that mean? If we take a look, let's apply to this example. Here we have a log of 10 is equal to two because remember, Long based 10 100 is really tend to the to the log based 10 of the 10 will cancel out, and then this expo have become my answer of to when we do the inverse or the anti log. What that really means is that we have 10 to the to, which is equal to 100. Okay, so when we take the anti log off a number, what happens is that your ex becomes your answer based on the original log function. Now, when we come in tow into basically the presence of having to use the antilock function if we take a look here normally, when we're dealing with situations dealing with buffers. That's when we might see the use of the anti log function. So for this example here, they're telling us that the Henderson Hasselbach equation is a useful equation for the determination of the ph of a buffer. Now, buffers are incredibly important in chemistry as well as in biology. Are blood is based on the concept of a buffer? Ah, buffer prevents the pH of a solution in this case, our blood from becoming too acidic or two basic very quickly. So if you ate something that was acidic and you didn't have buffers in your blood and your blood will become very acidic very quickly and you become acid attic. If you ate something that was very basic, then you would have basic blood, which again would cause harm to your organs. That's why our blood has within it carbonic acid and sodium bicarbonate to balance one another out. We're gonna say with buffers we have the Henderson has a back equation, and it basically gives us a ratio off base toe acid within a solution and specifically our conjugate base toe are weak acid. Now, using this formula, we're gonna see how the anti log function plays a role in finding the answer that we need. We need to figure out the ratio they tell us of conjugal based a weak acid. They tell us the P H is equal to 417 They tell us the P K is equal to 383 We're gonna plug those numbers in, so Ph equals 4.17 My Pekka is 3.83 plus log of my conjugate base over my weak acid, which I'll abbreviate SCB over W A. We're going to subtract 33 from both sides, so it's gonna give me 34 equals log of conjugate base over weak acid. So here we just want to find the ratio by itself. So we need to take the anti log in order to get rid of this log function here. So when I take the anti log of both sides that will cancel out this and then the anti log will raise this toe a power so tend to the 0.34 power gives me the ratio of conjugate base over weak acid. When we punch that into our calculators, we get 2.18776 as our answer for the ratio. So the closest answer to this would be options, see, once we round. So what this ratio was telling me and remember, ratio means we'd have two numbers. This number would be over one. So what this answer is telling me? It's telling me for everyone weak acid component. I have 2.18776 off my conjugate base that be the ratio in terms off the distribution between my conjugate base and my weak acid.