Logarithmic Inequalities and Solutions

This video tutorial covers solving logarithmic inequalities, starting with a review of logarithmic expressions and their properties. It explains the rules for solving inequalities, including the impact of the base being greater or less than one. The tutorial provides multiple examples, illustrating how to find solution sets using number lines and set builder notation. It also addresses compound inequalities and offers tips for ensuring logarithms are defined correctly.

What is the base of a natural logarithm?

• 10

• 2

• e

• 1

In a logarithmic inequality, what happens to the inequality symbol when both sides are multiplied by a negative number?

• It becomes undefined

• It becomes an equality

• It reverses

• It remains the same

If the base of a logarithm is greater than 1, how does the inequality symbol behave?

• It remains the same

• It becomes undefined

• It becomes an equality

• It reverses

For a base less than 1, what happens to the inequality symbol in a logarithmic inequality?

• It becomes undefined

• It becomes an equality

• It reverses

• It remains the same

What is the solution set for the inequality log base 3 of x < 4?

• 0 < x < 81

• x > 81

• x < 81

• x > 0

In the example with two x's, what is the solution set?

• 0 < x < 3

• x < 3

• x > 0

• x > 3

What is the solution set for the quadratic inequality example?

• x > 0

• x < 0

• 0 < x < 6

• x > 6

For a base of 0.5, what is the solution set for the inequality log base 0.5 of x > 5?

• x > 1/32

• x < 0

• x < 1/32

• x > 0

What is the solution set for the compound inequality example?

• 1/1000 < x < 1000

• x > 0

• x < 1/1000

• x > 1000

What should you be careful about when solving logarithmic inequalities?

• None of the above

• The base value

• The inequality symbol

• Both base and inequality symbol