Logarithmic Equations and Quadratics

This video tutorial demonstrates how to solve a logarithmic equation that requires the use of the quadratic formula. It begins by combining logarithms and converting the equation into an exponential form. The tutorial then explains how to solve the resulting quadratic equation, including using the quadratic formula when factoring is not possible. Finally, it discusses checking the solutions to ensure they are valid within the context of the original logarithmic equation.

What is the first step in solving a logarithmic equation that involves a quadratic formula?

• Convert the equation to a linear equation

• Combine the logarithms and convert to an exponential equation

• Directly apply the quadratic formula

• Factor the equation immediately

When combining two logarithms with the same base, which property is used?

• Product Property

• Power Property

• Change of Base Property

• Quotient Property

After converting the logarithmic equation to a quadratic equation, what is the next step?

• Apply the quadratic formula immediately

• Graph the equation

• Set the equation to zero and check if it is factorable

• Solve for x using substitution

What are the values of A, B, and C in the quadratic equation derived from the logarithmic equation?

• A = 1, B = 2, C = -9

• A = 3, B = 1, C = -7

• A = 2, B = 3, C = -5

• A = 1, B = 1, C = -11

What is the discriminant value used in the quadratic formula for this problem?

• 45

• 43

• 42

• 44

What is the simplified form of the square root of 45?

• 5 square root 3

• 3 square root 5

• 9 square root 5

• 5 square root 9

Which solution is valid for the logarithmic equation based on the properties of logarithms?

• x = -1 plus 3 square root 5 divided by 2

• x = -1 minus 3 square root 5 divided by 2

• Both solutions are valid

• Neither solution is valid

Why is the solution x = -1 minus 3 square root 5 divided by 2 excluded?

• It results in positive arguments for the logarithms

• It results in zero arguments for the logarithms

• It is not a real number

• It results in negative arguments for the logarithms

What must be true about the arguments of the logarithms in the solution?

• They must be negative

• They must be zero

• They must be positive

• They can be any real number

What is the approximate decimal value of the valid solution?

• 2.8541

• -3.8541

• 1.8541

• 0.8541