To familiarize ourselves with the properties we will first expand the following logarithms. (Assume all variables are positive.)

**Expand**.

*n*th roots within the argument of the logarithm. To simplify these, first change the root to a rational exponent then apply the power rule.

**Evaluate**

Expanding is useful for learning the rules and properties associated with logarithms but as it turns out, in practice, condensing down to a single logarithm is the skill that we really need to focus on.

**Rewrite as a single logarithm (condense)**.

**Tip**: When simplifying these down to one logarithm use only one operation at a time and work from left to right. Combining or skipping steps usually leads to mistakes. Do not race, work slowly, and pay attention to notation.

**Simplify**.

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