The Basics Examples

Evaluate log₂8.

Ask yourself 2 to what power is 8? We won't tell anybody you were talking to yourself. The answer is 3 because 2 × 2 × 2 = 8.

Evaluate log₁₂ 999.

This is a quick conversion to base 10 because most of our calculators don't let you choose what base you want. On your calculator, divide log 999 by log 12. The logarithm is 2.779 (rounded to 3 decimal places).

Rewrite log ab²c² as a sum of logarithms with no exponents.

We need to use the properties of logarithms. The good ol' product rule and power rule for now. We should first notice that we want to take the logarithm of the product of a and b² and c². Watch and learn.

log ab²c² = log a + log b² + log c²

Now we will apply the power rule.

log a + log b² + log c² = log a + 2 log b + 2 log c

And, that's it. We're done. (Applause.)