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Find the exact value of each expression.

(a) $ \log_5 \frac{1}{125} $

(b) $ \ln (\frac{1}{e^2}) $

a) $-3$

b) $-2$

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Johns Hopkins University

Missouri State University

Campbell University

Harvey Mudd College

to evaluate these log rhythms, you might want to start by changing how they look just a little bit. So when you see 1/1 25 you should think of that as 1/5 cubed and 1/5 cubed is the same as five to the negative third power. So now you're ask yourself five toe what power equals five to the negative third power. Well, that would have to be negative. Three, Similarly, on the next one. When we see the natural log of one over e squared, we could think of it and rewrite it as the natural log of e to the negative second. Now, you ask yourself, e toe what power would give me e to the negative second. Well, that would have to be the negative second power.