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\nMaster Evaluating a Logarithmic Expression using the Properties of Logarithms\n

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\n\nPublisher:\n\nBrian McLogan\n\n\n
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\nWelcome, ladies and gentlemen. So what I'd like to do is show you how to evaluate some logarithmic expressions when we're just kind of using the properties of logarithms. And what I did here is-- actually, let me step out of the camera...\nWelcome, ladies and gentlemen. So what I'd like to do is show you how to evaluate some logarithmic expressions when we're just kind of using the properties of logarithms. And what I did here is-- actually, let me step out of the camera here real quick.

What I did is I highlighted some very common logarithmic properties that we're going to be using to help us evaluate these logarithmic expressions. Now, some of these you might be familiar with. Some of these might be a little bit new.

But using these properties is going to greatly help us evaluate logarithms because what we're going to do or what you've previously done is learn how to evaluate a logarithm for what exactly a logarithm means. Actually, you should already know that.

So for instance, if I said, let's use the basic one. If I said log base 2 of 4, hopefully you understand that the answer to this is going to be 2, and the reason being is because what the question is asking is 2 raised to what number gives you 4?

Well, we know the answer is going to be 2. Well, again, if I write 2 raised to 2 equals, what does that equal? So again, I'm asking 2 raised to what number is equal to 2? Well, hopefully we understand that that number is going to be 1.

Log base b of b is just equal to 1. Now, there's another thing you guys can think about. Any number you can always raised to the first power. So log base 2 of 2 to the first power, you could also think of that as equaling 1 from there.

So let's go back to a step further. Let's go back. And what about if I wrote this as 2 raised to the fourth power? Now let's change this to a 3. Let's see what this would be.

Now, log base 2 of-- oops, now, these aren't same powers, so that doesn't follow that rule, does it? So let's change this to 2. And now let's raise this to the third power.

So 2 base 2 of 2 raised to the third power. Well, by using my previous logic of 2 base 2 of 2 equals 1 and up to 1, then therefore we could probably say that this is going to equal 3. Now let's go ahead and verify our answer here. If I had 2 cubed, that's 8. So log base 2 of 8-- that's really the same thing.

Well, 2 raised to what number gives you 8? Well, 2 times 2 is 4. 2 times 2 times 2 is 8, which is 3. So therefore, this you can see how this rule is going to apply, as well. So log base b of b raised to the power is going to just be equal to whatever that power.

So the last property we're just going to look at is basically kind of like the exact [INAUDIBLE] this. If I have the base b and that's raised to my log base b of x, therefore then that's just going to equal x. And again, we can just look at this. I'll just use some numbers as a property here.

So let's use 2. Let's do log base 2 of-- again, let's do 4. Or let's do 8 again. That's fine. Let's use 8.

Now, we know 2 raised to what power gives you 8? That's 3. Or log base 2 of 8 is 3 because 2 raised to what power give you 8? That's 3. So in reality, that's going to be 2 to the third power, which is 8. Or based off of that logarithm, based on that rule, when we have 2 raised to the log base of 2, we know that the answer's going to be 8.

So you could either look at the best thing to do is I wanted to spend some time since these are going to not take that long, these are not going to take-- I wanted to spend some time explaining you and showing you how these rules work.

Now, let's get into some of these examples. So for the first example, we have log of 10. Now, make sure when we see log of 10, we understand that that is log base 10 of 10. So therefore, I'm taking the log. I have the same base as what I'm evaluating the logarithm for.

So therefore, by using this rule, I know that that is going to evaluate to equal 1. Then we introduce the natural logarithm, which is e.\n
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Media Length
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7:29
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Grade
12th - Higher Ed
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Subjects
Math
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Source:
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\nBrian McLogan\n\n
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Date
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2016
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Language
English
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