Use a graph or table to solve the following inequality: 2 log x − 4 log 3 > 0.

1. x > 9
2. 0 < x < 9
3. x < 9
4. x > 0

A
Correct! Any value of x greater than 9 makes the left side of the inequality greater than 0.

B
Incorrect. Values of x between 0 and 9 make the left side of the inequality less than 0.

C
Incorrect. When x is less than 9, the left side of the inequality is less than 0. The left side of the inequality is not defined for x-values less than 0.

D
Incorrect. While the left side of the inequality is defined for any x-value greater than 0, there is a more specific domain that satisfies this inequality.

Use a graph or table to solve the following inequality: log₅ x < 3.

1. 0 < x < 125
   Correct! Any values of x between 0 and 125 make the left side of the inequality less than 3.
2. x < 125
   Incorrect. The left side of the inequality is not defined when x < 0.
3. x ≥ 125
   Incorrect. When x is greater than 125, the left side of the inequality is greater than 3.
4. No solution
   Incorrect. There is a specific domain that satisfies this inequality.

Use a graph or table to solve the following inequality: log(5 – x) – log 7 ≥ 0.

1. x > -2
   Incorrect. When x is greater than -2 , the left side of the inequality is less than 0.
2. x ≥ -2
   Incorrect. When x is greater than -2, the left side of the inequality is less than 0.
3. x ≤ -2
   Correct! Any value of x less than or equal to -2 makes the left side of the inequality greater than or equal to 0.
4. x < -2
   Incorrect. Notice that the inequality you are solving is greater than or equal to.

Use a graph or table to solve the following inequality: 2 log x < log (2x – 1).

1. x < 1
   Incorrect. While x = 1 makes the two sides of the inequality equal, the left side of the inequality is always greater than the right side of the inequality.
2. x > 1
   Incorrect. While x = 1 makes the two sides of the inequality equal, the left side of the inequality is always greater than the right side of the inequality.
3. All real numbers
   Incorrect. While x = 1 makes the two sides of the inequality equal, the left side of the inequality is always greater than the right side of the inequality.
4. No solution
   Correct! Even though the two sides of the inequality are equal at x = 1, there are no values of x that make the left side of the inequality less than the right side of the inequality.

Use a graph or table to solve the following inequality: log₄(x – 1) + log₄(x + 1) < log₄6.

1. x < 2.646
   Incorrect. The left side of the inequality is no longer defined for x-values less than 1.
2. x > 2.646
   Incorrect. When x > 2.646, the left side of the inequality is greater than the right side of the inequality.
3. 1 < x < 2.646
   Correct! For the left side of the inequality to be defined, x must be greater than 0. When x is less than 2.646, the left side of the inequality is less than the right side of the inequality.
4. No solution
   Incorrect. There is a specific domain that satisfies this inequality.