Logarithmic Equations and Properties

The video tutorial covers solving logarithmic equations, starting with an introduction to the topic. It explains the quotient rule of logarithms, which allows rewriting a subtraction of logarithms with the same base as a single logarithm. The tutorial then demonstrates using one-to-one properties to equate expressions and solve the equation. Finally, it verifies the solution by checking if the result satisfies the original equation.

What is the first step in solving a logarithmic equation?

• Apply the power rule

• Identify the properties to use

• Convert to exponential form

• Simplify the equation

Which rule allows you to rewrite a subtraction of logarithms as a single logarithm?

• Quotient rule

• Product rule

• Power rule

• Change of base rule

What is the result of applying the quotient rule to log base 2 of (x+4) - log base 2 of 4?

• log base 2 of (x+4) * 4

• log base 2 of (x+4) / 4

• log base 2 of (x+4) + 4

• log base 2 of (x+4) - 4

What does the one-to-one property of logarithms state?

• If two logs with the same base are equal, their arguments are equal

• If two logs with different bases are equal, their arguments are equal

• If two logs with the same base are equal, their bases are equal

• If two logs with different bases are equal, their bases are equal

What is the significance of the one-to-one property in logarithms?

• It allows conversion to exponential form

• It ensures the arguments of equal logs are equal

• It helps in simplifying logarithmic expressions

• It changes the base of the logarithm

How do you eliminate the fraction in the equation x+4/4 = x+3?

• Divide both sides by 4

• Multiply both sides by 4

• Add 4 to both sides

• Subtract 4 from both sides

What is the equation after eliminating the fraction in x+4/4 = x+3?

• x + 4 = 4x + 12

• x + 4 = x + 12

• x + 4 = 4x - 12

• 4x + 4 = x + 12

What is the next step after obtaining the equation x + 4 = 4x + 12?

• Multiply both sides by 3

• Get all variables on one side

• Subtract 4 from both sides

• Add 12 to both sides

What is the value of x after solving the equation 4 = 3x + 12?

• x = -3/8

• x = 3/8

• x = -8/3

• x = 8/3

Why is it important to verify the solution in a logarithmic equation?

• To simplify the equation further

• To check if the solution satisfies the original equation

• To confirm the base of the logarithm

• To ensure the solution is positive