Algebra 2 - solving an equation with the equality of logarithms log3 (x^2 - 15) = log3 (2x)

The video tutorial explains the rule of equality with logarithms, demonstrating how if log base B of X equals log base B of Y, then X equals Y. It applies this rule to solve a specific equation involving logarithms and transitions into solving quadratic equations. The tutorial discusses different methods for solving quadratics, including factoring, completing the square, and using the quadratic formula. It emphasizes the usefulness of factoring and applies the zero product property to find solutions. The session concludes with a summary of the process and solutions found.

What is the rule of equality for logarithms with the same base?

• If log base B of X equals log base B of Y, then X is not equal to Y.

• If log base B of X equals log base B of Y, then X is less than Y.

• If log base B of X equals log base B of Y, then X is greater than Y.

• If log base B of X equals log base B of Y, then X equals Y.

What type of equation is formed when solving the logarithmic equality in the example?

• Quadratic equation

• Linear equation

• Exponential equation

• Cubic equation

Which method is NOT mentioned as a way to solve the quadratic equation?

• Factoring

• Completing the square

• Graphing

• Quadratic formula

What is the factored form of the quadratic equation X^2 - 2X - 15 = 0?

• (X + 3)(X - 5)

• (X - 3)(X + 5)

• (X + 5)(X - 3)

• (X - 5)(X + 3)

What are the solutions to the equation X^2 - 2X - 15 = 0 after factoring?

• X = 5 or X = -3

• X = -5 or X = 3

• X = -5 or X = -3

• X = 5 or X = 3