So this right over here is 2 to the sixth power, is equal to 64. The exponent that I have to raise 2 to, to get to 64." So 2 to the first power is 2, 2 to the second power is 4, 8, 16, 32, 64. So what does this evaluate to? Well once again we're asking ourselves, "well this will evaluate to the exponent that I have to raise this base 2, and you do this as a little subscript right here. Let's say I had, I dunno, log, base 2, of 64.
So if someone says "what power do I have to raise 6 to- this base here, to get to 216?" Well that's just going to be equal to 3. So this is 6 to the third power is equal to 216. What will this evaluate to? Well we're asking ourselves, "what power do we have to raise 6 to, to get 216?" 6 to the first power is 6, 6 to the second power is 36, 36 times 6 is 216. So let's try a larger number, let's say we want to take log, base 6, of 216. Let's do several more of these examples and I really encourage you to give a shot on your own and hopefully you'll get the hang of it. Log, base 3, of 81, is equal to- I'll do this in a different colour. Well what power do you have to raise 3 to to get to 81? Well let's experiment a little bit, so 3 to the first power is just 3, 3 to the second power is 9, 3 to the third power is 27, 3 to the fourth power, 27 times 3 is equal to 81. The power I need to raise 3 to to get to 81. To do it this way, to say that 'x' is the power you raise 3 to to get to 81, you had to use algebra here, while with just a straight up logarithmic expression, you didn't really have to use any algebra, we didn't have to say that it was equal to 'x', we could just say that this evaluates to the power I need to raise 3 to to get to 81.
But you didn't necessarily have to use algebra. Why is a logarithm useful? And you'll see that it has very interesting properties later on. So if you want to, you can set this to be equal to an 'x', and you can restate this equation as, 3 to the 'x' power, is equal to 81. What would this evaluate to? Well this is a reminder, this evaluates to the power we have to raise 3 to, to get to 81. So with that out of the way let's try more examples of evaluating logarithmic expressions. This is saying "hey well if I take 2 to some 'x' power I get 16'." This is saying, "what power do I need to raise 2 to, to get 16 and I'm going to set that to be equal to 'x'." And you'll say, "well you have to raise it to the fourth power and once again 'x' is equal to 4. Log, base 2, of 16 is equal to what, or is equal in this case since we have the 'x' there, is equal to 'x'? This and this are completely equivalent statements. Now the way that we would denote this with logarithm notation is we would say, log, base- actually let me make it a little bit more colourful. And this is what logarithms are fundamentally about, figuring out what power you have to raise to, to get another number. So for example, let's say that I start with 2, and I say I'm raising it to some power, what does that power have to be to get 16? Well we just figured that out. We know that we get to 16 when we raise 2 to some power but we want to know what that power is. But what if we think about things in another way. 2 multiplied or repeatedly multiplied 4 times, and so this is going to be 2 times 2 is 4 times 2 is 8, times 2 is 16. If I were to say 2 to the fourth power, what does that mean? Well that means 2 times 2 times 2 times 2.
#Solving logs how to#
So we already know how to take exponents. Let's learn a little bit about the wonderful world of logarithms.
0 kommentar(er)
