Calculating Logarithms

Video Transcript

"Let's look at calculating logarithms. I find that logarithms are a topic that intimidates a lot of students, just because the word logarithm is just different, it's just weird. It sounds kind of like another language; we don't use it all the time. But really logarithms are really pretty straightforward once you see it, once it's explained clearly. So, let's take a look. Really logarithms are just kind of like another word for using exponents. So here's an example: so this says log base five of twenty-five equals two. What this really means is--you kind of just have to memorize who goes where, what each spot represents. What this really means is five--so the number that's the base, five--to the two, so two being the exponent, equals twenty-five. That's what a logarithm really means. It means this number, to the this power, equals that. That's how we read it. That's all it is; that's it, that's the whole deal. Then we go from there. That's the foundation of logarithms. So let's take an example. If I said log base three of nine equals what? So you'd have to ask yourself: three to the what is nine? And the answer is two. Three squared is nine. So log base three of nine is two. This expression equals two. You could cross that out and write a two. That's what this is, that's what that word means. One last thing: if you see a log with no base written, so log one hundred--actually let's do a thousand--so log of a thousand, if they don't tell you the base it's an assumed ten. That's the way we work, that's the agreement that mathematicians have. So if there's no number written here, it's like it's a ten. So you ask yourself ten to the what is a thousand? And the answer is three. Ten cubed is a thousand. So log base ten of a thousand, that whole expression equals or is, another word for three."