**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 1:**

**Example 5:** Suppose that a base is 8 and exponents are 6, .5, and 3. We could
simplify the exponential problem by
combing the exponents and writing the problem as .

The same is true of logarithms. Suppose you wanted to simplify the expression . You could so by writing

**Note:** The two expressions and are equivalent expressions. Recall that equivalent expressions
do not look the same but will result in the same answer.

**If you would like to work a problem, click on
Problem. **

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