Solving Logarithmic Equations with Logs on Both Sides

The video tutorial covers solving linear and quadratic logarithmic equations. It begins with linear equations, demonstrating how to find variable values by dropping logs when they appear on both sides. The tutorial emphasizes checking solutions by substituting them back into the original equations. It then transitions to quadratic logarithmic equations, explaining the use of log properties and methods like the X method and quadratic formula to find solutions. The importance of verifying solutions to ensure they don't result in negative values inside logarithms is highlighted throughout.

What should you do when logarithms on both sides of an equation have the same base?

• Drop the logarithms

• Multiply the logarithms

• Divide the logarithms

• Subtract the logarithms

After solving for 'p' in a logarithmic equation, what is the next step to ensure the solution is correct?

• Divide the result by 2

• Add 1 to the result

• Multiply the result by 2

• Substitute 'p' back into the original equation

How do you handle a subtraction sign within a logarithmic expression?

• Convert it to multiplication

• Convert it to division

• Convert it to addition

• Ignore the sign

What is the result of condensing log base 9 (-3x) - log base 9 (10)?

• log base 9 (7x)

• log base 9 (-3x + 10)

• log base 9 (-3x / 10)

• log base 9 (-30x)

In a quadratic logarithmic equation, what method is suggested if simplifying does not easily solve the equation?

• X method

• Y method

• Z method

• W method

What should be done when both sides of a quadratic logarithmic equation have the same log base?

• Cancel the logs

• Multiply the logs

• Combine the logs

• Subtract the logs

What is the correct solution process for the equation 3x^2 + 39x + 12 = 0 using the X method?

• Find factors of 156 that add up to 39

• Find factors of 12 that add up to 39

• Find factors of 36 that add up to 39

• Find factors of 108 that add up to 39

What is the correct simplification for -36/9?

• 3

• -4

• -3

• 4

After solving a quadratic logarithmic equation, what should you do to verify the solutions?

• Divide the solutions

• Add the solutions together

• Multiply the solutions together

• Substitute back into the original equation

What does the equation 3x - 1 = 0 solve to?

• x = 3

• x = -3

• x = -1/3

• x = 1/3