Logarithmic Functions

Jules Bruno
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the longer thick base 10 form represents the exponents that 10 must be raised in order to obtain that specific number. Now what does this really mean? Let's take a look at these examples here. So here we're looking at the power that we can raise 10 to and the answer that results. So 10 to the one is just 10 times one, which gives us 10. 10 of the four is just 10 times 10 times 10 times 10 which gives US 10,000 10 to the negative. One is equivalent to just saying 1/ right, because what it's really saying is 10 inverse. So that's 1/10. So that gives us 100.10 and then tend to the zero. Any number to the zeroth power equals one. How does this relate to my log function? Well, here we have long of 10 gives us one really what this is saying. It's saying that 10 toe what number gives me? Give me one. The answer would be one. Here. Log off. 10,000. All right. So think of it like this. We have log of 10,000. So that's really log of 10 to the four whatever the number is here. Because, remember, this is long based 10. What happens here is that this will cancel out with this. So we get four left at the end here when we get log off 0.10. What does that really mean? That really means log off 10 to the negative one. So this council's out with this and gives us negative one. Then we have log of one. Right? So you'd say here. So log based 10 and then tend to the one here. Oh, will tend to zero. You're actually sorry. Equals zero. So that's what's really going on here. And if we have log off 10 think that as log based 10 and then tend to the one equals one. So we're just converting each of these values by 10 to some power. The log portion cancels out the 10 and lose behind the exponents as my final answer. That's how we can see log. I know you guys have calculators, but there may come a point where you have this within the math class or within an M cat or P cat or O A. T or D 80. Later on much later on after you've taken all these science courses where you have to understand these relationships. And this is how our log based function is connected to multiples of 10. Knowing that helps us to get to the answer. Now, understanding this, try to see if you can answer example one. So here we're gonna use this without a calculator. Try to do without a calculator to see what answer you get, and then afterwards come back, use a calculator and see if your answer Masters up matches up. I hope you guys a little bit for the first one. So here this law is getting distributed to the one end to the 10th of negative seven. Now, when that happens, what that means is we have long of one. And because they're multiplying, it really means that we're adding. So it's plus log of 10 to the negative seven. See if you guys can figure out what the answer is without using a calculator, come back and see if your answer matches up with mine.