Logs, Log Equations, & Graphs

Exponentials don't make tons of sense to most students, but at least they're just about something we've all seen before: exponents. Logs, on the other hand, are a whole new ballgame! They're hard to use, difficult to do in your head, and have no obvious use beyond the labyrinth of their own rules. And good luck plugging in points to help graphing them! Worst of all, they're easy to confuse with exponentials, especially when you're graphing them. So, throughout the videos below I focus on de-confusing the twisted sisters that are exponentials and logs.

Evaluating Logs & Solving Basic Log Equations

In this video I cover the basics of logarithms, starting with what the heck they are and how to "evaluate" them. That basically means doing "simple" logs in your head by rearranging them into exponentials, which believe it or not you'll look back fondly upon once you see these crazy log things.

Log Properties

This video is all about those three formulas that turn log addition into multiplication, subtraction into division, and coefficients into exponents. The examples I work involve condensing logs (turning a few into one) and expanding logs (the opposite).

Change of Base Formula

The change of base formula is something every student is confused by, but it's not so bad: it basically allows you to find logs on your calculator using bases other than e and 10. Once you see a few examples, the confusion will end.

Solving Difficult Log Equations

At the end of each problem we'll do the "curly q" we'd use to solve an equation with only one log in it, but first we'll have to use all those log properties to condense two or three logs into one. I also talk about the common mistake you don't want to make.

Graphing Logs

Let's face it, graphing logs is a dog. The worst. But to conquer these beasts you must simply never forget, ever ever, that logs always and only have vertical asymptotes. (awkward silence) We get into some other transformation stuff too.

Graphing Logs vs Exponentials (free)

This is the biggest confusion my tutoring students have with Logs & Exponentials -- telling log graphs apart from exponential graphs, and knowing how to graph each -- so this video will probably help you too! (Hint: it will involve vertical asymptotes and horizontal asymptotes, and which goes with what.)

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