Order Equation Log For Free

Hi guys! I'm Nancy and I'm going to show you how to solve logarithmic equations. In my other logarithms video I warned you that solving log equations could be a whole other video, so here we are. Let me show you how to solve them. OK, so a quick recap, in my other logarithms video I showed you some simple log equations that just had one log in them and equaled a number. OK, so every log is connected to an exponential form. Logs and exponentials are opposite operations of each other, and the best way to figure out a log is to rewrite it into exponential form, and solve for X. And in my other video, "Logarithms... How?", I showed you how to rearrange the log into exponential form, and solve for X. Basically, it's just the little base number, raised to the power of the number on the right side, equals the middle number, the argument or the number that's left, so... base to the right side equals the middle, base to the right side equals middle. If you don't remember how to do this you can jump to my other video, "Logarithms... How?" There was talk of memory tricks, like little to the right equals middle. There was talk of snails with counter clockwise spiraling shells, it was real party. But basically this is the simple kind of log equations. What if it's not so simple? What if it's more complicated? You say, like more that one log, a log equals another log. Several logs equal a number. Many logs, some of them with numbers multiplied out front.. What do you do? And what do you do if you see something like "check your solutions?" Or if your teacher says, "Check for extraneous solutions" or "check your answers." How do you do that? I'll show you. And I'll also show you the log properties, which are what you need to simplify and condense, and solve more complicated equations like that. So that would be like the power property, quotient property, product property, equality property, all of those. So my other video gave you a taste of solving log equations at the end, and now I'm going to give you a whole meal. But if you see the kind that you're working on you can skip ahead. So just check the description for the time to jump to. Let me show you how to solve. Alright, say you have a log on each side of the equation. It's getting more complicated, but don't worry, don't panic, because actually really simple, if the logs have the same base you can just set the insides of the logs equal to each and solve. So this is the equality property and it's just like I was saying, if the little bases are the same you can take the insides of the log and set them equal to each other. By the way this is for little bases that are positive and not equal to one. But anyway, if the bases are the same, you can set the insides equal, and I know what you're thinking, "What bases?" "I don't see any bases." Yeah, they're not explicitly written here. If you don't actually see them, it's implied to be 10, the common log. So that's like the default, and we can just go ahead and...