Solving Logarithmic Equations and Inequalities: Category 3 Challenge

What is the key concept behind the property of equality for logarithmic functions?

• Logarithms on both sides must have different bases.

• Logarithms on both sides must have the same base.

• Logarithms on both sides must be equal to zero.

• Logarithms on both sides must be positive.

In the equation log base 7 of X equals log base 7 of 3, what is the value of X?

• 0

• 1

• 3

• 7

Why is it important to check solutions when solving logarithmic equations?

• To ensure the solutions are integers.

• To ensure the solutions are positive.

• To ensure the solutions are within the domain of the logarithmic function.

• To ensure the solutions are even numbers.

In the equation log base 3 of (x^2 - 15) equals log base 3 of (2x), what is the valid solution for x?

• 2

• 5

• 3

• 0

When solving logarithmic inequalities with a greater than sign, what can be ignored?

• The exponents

• The bases

• The coefficients

• The constants

In the inequality log base 2 of (4x - 10) > log base 2 of (x - 1), what is the solution for x?

• x > 5

• x > 2

• x > 4

• x > 3

What additional step is required when solving logarithmic inequalities with a less than sign?

• Ensuring the solutions are even numbers.

• Ensuring the solutions are integers.

• Ensuring the solutions do not violate the domain restriction.

• Ensuring the solutions are positive.

In the inequality log base 2 of (2x + 1) < log base 2 of (x + 4), what is the valid range for x?

• x < 3

• x < 2

• x < 0

• x < 1

What is the main focus of the classwork due on Friday night?

• Solving exponential equations

• Solving linear equations

• Solving logarithmic equations and inequalities

• Solving quadratic equations

Which category of problems involves rewriting logarithmic equations in exponential form?

• Category three

• Category one

• Category two

• Category four