# The Binary System 4u Review

### Logarithms How mathbff

Hi guys, I'm Nancy, and I'm going to show you logarithms. quot;Logarithmsquot; sounds a little pretentious so I'm just gonna call them quot;logsquot; and here are the kinds I'm gonna show you. So if you see something up here that looks like the kind you're trying to figure out you can use the links in the tutorial or the description to skip ahead. So I'm gonna show you first the basic kind of logs then I'll show you some weirder kinds

if you have a log of a negative number, 0, 1, or a fraction. I remember hating the fraction kind. And then I'll show you natural logs which are a special kind of log. And finally, some even weirder logs and by that I mean if you have an x in the log part of your expression or if you have to use the changeofbase formula. So let me show you the basic ones.

OK, what if you have a basic log expression like thisé What is thaté How do you even read that expressioné The way you read it is quot;log, base 3, of 9quot;. But how do you evaluate ité Or what if you have to simplify thaté How do you do ité There are a few ways. One way, if you're the kind of person who loves to do things in your head

you can just think to yourself quot;3, raised to what power, gives me 9équot; And if you can do it that way, more power to you, you are cooler than the rest of us. But for all the rest of us usually the easiest way the fastest way is to rewrite this into exponential form. And I will show you how to do that. But the first thing you should do

is if this doesn't already equal something, make it equal to x. And there's a reason for that. Because you're going to rearrange this and connect it to an exponential version. How do you do thaté There's a pattern you can use. And here's the pattern. To rewrite this into exponential form so that you can find the answer you start with this little base that I circled. This is the base of your log expression.

Start there, and move in this direction of the arrow. and raise that base to the power of what's on the right side. So the base 3. raised to the power of the right side, which is x. equals.set it equals. 9, the middle number, or the other number that's left that you haven't used. Alright, so I've just rearranged into exponential form with that pattern. Some people think of it as quot;little, to the right, equals middlequot;