And now this is interesting,Ĭuz if I'm multiplying by log of C, and dividing by log of C, both of them base 10, well those are going to cancel out and I'm going to be left with log base 16, sorry log base 10 of 16 over, over log base 10 of two. These little 10's here if it makes you comfortable. So this first one, this first one I could write this as log base 10 of 16, remember if I don't write the base you can assume it's 10, over log over log base 10 of C, and we're going to be multiplying this by, now this is going to be, we can write this as, log base 10 of C, log base 10 of C over, over log base 10 of two. So this one, once again it might be nice to re-write these, each of these, as a rational expressionĭealing with log base 10. So I've log base C of 16, times log base two of C, alright. Now let's try to, now let's try to tackle So actually not so magical after all, but it's nice to see howĮverything fits together. And if I were to say log base 64 of four, well now I'm going to have to raise that to the one third power. So if I had log base four of 64, that's going to be equal to three. For example, we know thatįour to the third power is equal to 64. Then it starts to make sense, especially relative toįractional exponents. Little bit magical until you actually put some This is log base B, what exponent do I have to raise B to to get to four? And then here I have what exponent do I have to raise four to to get to B? Now it might seem a If I take the, If I take the reciprocal of a logarithmic expression, I essentially have swapped the bases. So we have a pretty neat result that actually came out here, we didn't prove it for any values, although we have a pretty general B here. This is the same thing as log base four of B, log base four of B. Other direction now, using this little tool we established at the beginning of the video. Log of B over log of four, which of course is just going to be log of B over log of four, I just multiplied it by one, and so we can go in the So this is going to be equal one times the reciprocal of this. Now if I divide by some fraction, or some rational expression, it's the same thing as multiplying by the reciprocal. Write the base there we can assume that it's base 10, log of four over log of B. So this is going to be equal to, this is going to be equal to one, divided by, instead of writing it log base B of four, we could write it as log of four, and if I just, if I don't Well let's use what we just said over here to re-write it. This is one divided by log base B of four. This yellow expression, this once again, is the same thing as one divided by this right over here. Useful thing to know if you are dealing with logarithms. So here you're saying theĮxponent that I have to raise A to to get to B is equal to the exponent I have to raise 10 to to get to B, divided by the exponent Peoples calculators or they might be logarithmic So 10 is the most typical one to use and that's because most This could be base nine,īase nine in either case. Well this is going to be true regardless of which base you chooseĪs long as you pick the same base. Now you might be saying wait, wait, wait, we wrote a logarithm here but you didn't write what the base is. When I'm talking about change of base, I'm saying that if I have the log base, and I'll color code it, log base A of B, log base A of B, this is going to be equal to log of B, log of B over log of A, over log of A. Logarithmic expressions, you might be able to You think about how you might be able to change theīase of the logarithmic, or the logarithms or the And I'll give you a hint inĬase you haven't started yet. Video and see if you can re-write each of these logarithmic expressions in a simpler way. And what I want you to do, like always, pause the Two different logarithmic expressions here, one in yellow and one
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |