**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 4:** Suppose that a base is 4 and exponents are a, b, and c. 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 as , providing *x* > 0, *y*>0, and *Z*>0..

**Note:** The two expressions and
are equivalent expressions. Recall that equivalent expressions do not look
the same but will result in the same answer is you substitute a value for x,
for y, and for z in both expressions. Let's try it. Suppose x = 10, y = 15,
and z = 20. Then

and

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

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