Find the Domain log base 7 of x^2-9

Problem

(log_7)(x2−9)

Solution

1. Identify the condition for the domain of a logarithmic function. The argument of a logarithm must be strictly greater than zero.

argument>0

2. Set up the inequality for the given expression.

x2−9>0

3. Factor the quadratic expression using the difference of squares formula.

(x−3)*(x+3)>0

4. Determine the critical points by setting the factors equal to zero.

x=3,x=−3

5. Test the intervals created by the critical points: (−∞,−3) (−3,3) and (3,∞)

For *x<−3,(−)*(−)=(+)

For −3<x<3,(−)*(+)=(−)

For *x>3,(+)*(+)=(+)

6. Select the intervals where the product is positive to satisfy the inequality.

x<−3* or *x>3

Final Answer

Domain:(−∞,−3)∪(3,∞)

Want more problems? Check here!