Solving Logarithmic Equations with Logs on Both Sides

This video tutorial covers solving logarithmic equations with logs on both sides of the equal sign. It explains the process of condensing each side to a single logarithm, canceling out logs with the same base, and solving the resulting equation. The tutorial emphasizes checking for extraneous solutions, as logarithms of negative numbers are invalid. Two examples are provided: the first involves basic operations, while the second is more complex, involving quadratic equations. The video concludes with a review of the solutions' validity.

What can be done when logarithms on both sides of an equation have the same base?

• Multiply the bases

• Add the bases

• Set the arguments of the logarithms equal

• Subtract the arguments

What signifies division in a logarithmic expression?

• Addition

• Subtraction

• Exponentiation

• Multiplication

How do you remove a variable from the denominator in an equation?

• By adding

• By subtracting

• By multiplying

• By dividing

What is the result of taking the square root of x squared?

• 2x

• Positive or negative x

• x

• -x

Why is negative 3 not a valid solution in the first example?

• It simplifies the equation to zero

• It results in the log of a negative number

• It makes the equation undefined

• It results in a positive logarithm

What does addition signify in a logarithmic expression?

• Division

• Exponentiation

• Subtraction

• Multiplication

How do you solve a quadratic equation in logarithmic problems?

• By subtraction

• By factoring

• By division

• By taking logarithms

What property is used to solve for variables in factored form?

• Distributive property

• Quadratic formula

• Logarithmic property

• Zero product property

Why was negative 2 not a valid solution in the second example?

• It makes the equation undefined

• It results in the log of a positive number

• It simplifies the equation to zero

• It results in the log of a negative number

What is the final valid solution for the second example?

• x = 3

• x = -2

• x = -3

• x = 2