Calculus: Problems and Solutions

There are some properties of logarithms that you absolutely must know to get through calculus. Most students shriek or faint when they see a logarithm, but if you learn these simple rules they become much easier to work with. Get a little practice, and you’ll be on your way to mastering logarithms!

All you really need to know are two rules: first, logs turn multiplication into addition:

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Second, taking the log of a power turns into multiplication by the exponent:

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From these, we can deduce a rule for quotients:

Here’s an exercise: how could I have shown the third rule if I only knew the first two?