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4-17 AIM3 8.6 Getting Started (Logarithmic Functions)

Added Apr 17, 2024 •

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hello again all right so have you ever used the log button on your calculator there it is next to the seven wonder if you might have used it and craft a chemistry class crafts what is it well will be formalizing that in the next video but let's just learn a little bit about it today so this long but and it is actually related to our original problem here why quilt into the extra you want to find the inverse we've had this discussion then we do the swap x equals 10 to the Y and we discuss how we're going to rewrite that using that L notation and so since the baser 10-week else up 10 of x equals what and the way you might want to think about this and Becky will want to think about this is that this face raise to that gives you this attention to the how were translating it and the lock button is one of these L functions for his that will formalize tomorrow and it is actually known as the common law algorithm has log or the L function base 10 log base 10 out of 10 in conventional used however actually notice I didn't try a base ten here I'm going to do it right now on this one if there's no base given then it is understood to mean base-ten you don't have to explain it to anybody it's log base 10 but we do you understand how to translate it so Member log base 10 means the base raised to something give you that value silver Napoli or log 1 well 10 to the what would give you one obviously zero how about log 10:10 to the first let's get this one how about a hundred but 210 square can you do some rocks lie very simple to figure out but others are not so this log20 well one thing we know is it must be between 1 and 2 and mathematicians back in the day has spent a fair amount of numerical time and time on their calculations figure out what locked when he was to whatever degree doctor said they wanted to place at three places 12 places out you can check on your calculator you do 10 to the 1.30 one no get very close to 21 really cool things this and we won't be discussing friend much year is well got log 20 how much we find log 200 and let me just tell you that it turns out it's too we know it's got to be bigger than 200 to 250 100 turns out it 301 we got ten times bigger here but we had one out here I wonder if you could predict with log 2001 I think get some hints on how long rhythms made calculations much much easier in the world will play around that some I want to just remind you a couple of our talk to you about a couple other done with logs so here we go Walker something equals -2 when I remember this is Phase 10 just this mess mean 10 to the negative 2 11 - 2 equals whatever this is us call it a so 10 to the negative two equals a 10 to the negative 2 exponent rules 1 / 10 squared or 1 / 100 Workhorse psychologist 0.01 we can take some number and raced to the negative but what about logs are what might that be that's obviously just being dumb number go by our definition and we should be able to say 10 to the some number equals 0 can you figure out what that might do how about this one over here I'll call it in so by definition 10 to the m must equal -10. Are you able to come up with a solution to that and the answer is I hope not cuz those situations are I think you can see where I'm going with this they are impossible turns out you can never have log0 or log the negative cuz will formalize this some day or so others can you take 10 to any power you'll never get zero if it's a positive number you get positive of course if it's an egg then you'll just do one over and again you got a positive so you just can't get it by the way back in the day if we want to find the log of something now if you want the log of 16 type log 16 back in the day read books and here's the cover of a book that you're nice to me I'll show you what the inside looks like cuz it's nice and scary and intimidating stuff we had to do anyway will formalize our discussion of logarithms and coming discussions

Uploaded by Brian Macky.

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4-17 AIM3 8.6 Getting Started (Logarithmic Functions)

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