**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 8: ** Simplify .

**Solution:** can be written . In its present form there is nothing
else we can do simplify the expression. Remember the rules of logarithms deal with products, quotients and powers, not sums or differences. Let's see if we can turn into a product. We can. The expression can be written in an equivalent form as the product of two factors: . Now the expression can therefore be written as .

Is the initial expression always
equal to the final expression ? **No!**

Note that the initial expression is valid only when . This means that if choose x > 6 or we choose x < 1, we can find the value of the initial expression.

You have to check/make sure that the number you take the logarithm of is positive. In our case, we must have that
*x ^{2} - 7 x +6* is strictly positive.

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