**Let a be a positive number such that a does not equal 1, let
n be a real number, and let u and v be positive real numbers.**

**Logarithmic Rule 3: .**

**Example 1: ** Find two ways.

**Solution:** Since can be written , the
expression can be written

which in turn can be written

We have

and

**Example 2:** Find .

**Solution:** The expression can be
written which in turn can be written . This last expression can be
rewritten using Rule 1 as

This represents 6 identical terms and we can
write the sum of the six terms as .

**Check:** The original expression can be written

The last expression can be written

**If you would like to review another example, click on Example.**

**Work the following problems and if you want to check your answer, click on answer.**

**Problem 1:** Find

**Problem 2:** Find

**Problem 3:** Simplify

**Problem 4:** Simplify

**Problem 5:** Simplify

**Problem 6:** Simplify . What assumptions must you make before you can begin work on this problem?

**Problem 7:** Simplify the following term completely

State the domain that makes your final answer equal to the original expression.

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