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In this lesson, we learn how to expand a single log into a sum or difference of logs. The basic properties include log of a to the n as n log a, log a times b as log a plus log b, and log a divided by b as log a minus log b. When expanding log x y divided by z, we get log x plus log y minus log z. Similarly, expanding log a squared b to the third c to the fourth d to the fifth gives us log a squared plus log b minus log c to the fourth minus log d to the fifth.