Logarithmic Inequalities and Exponentiation

The video tutorial covers solving logarithmic inequalities through five examples. It begins with an introduction to the topic, followed by step-by-step solutions to inequalities with different bases, including base 3, 4, 16, and more complex scenarios. The tutorial emphasizes the importance of understanding the properties of logarithms and exponents, and concludes with a call to action for viewers to subscribe for more content.

What is the first step in solving the inequality log base 3 of X < 4?

• Subtract 3 from both sides

• Exponentiate both sides with base 3

• Divide both sides by 3

• Add 4 to both sides

What is the solution to the inequality log base 3 of X < 4?

• X > 81

• X ≤ 81

• X < 81

• X = 81

In the second example, what is the base used for exponentiation?

• 4

• 3

• 2

• 5

What is the final solution for the inequality log base 4 of X ≥ 5?

• X ≥ 1024

• X < 1024

• X ≤ 1024

• X > 1024

What is the base used in the third example?

• 64

• 32

• 16

• 8

What is the final solution for the inequality log base 16 of X > 3/2?

• X = 64

• X < 64

• X ≤ 64

• X > 64

In the fourth example, what is the base used for exponentiation?

• 4

• 3

• 2

• 5

What is the final solution for the inequality log base 2 of (2X + 3) > log base 2 of (X - 2)?

• X > 1

• X > 5

• X > 3/2

• X > 2

In the fifth example, what is the base used for exponentiation?

• 2

• 3

• 4

• 5

What is the final solution for the inequality log base 5 of (X + 2) > log base 5 of (5X + 1)?

• -1/5 < X < 1/4

• X > 1/4

• X = 1/4

• X < -1/5