# RULES OF LOGARITHMS - RULE 3

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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