Logarithmic and Exponential Equations

The video tutorial explains how to solve a logarithmic equation by first recognizing the common log base, combining the logs using the quotient property, and converting the log equation into an exponential form. It then demonstrates solving the equation for x through algebraic manipulation and verifies the solution's validity by checking if it meets the conditions of the original equation.

What is the base of the common logarithms used in the given equation?

• 5

• 10

• e

• 2

Which property of logarithms is used to combine the two logs in the equation?

• Power Property

• Change of Base Property

• Product Property

• Quotient Property

What is the next step after combining the logarithms into a single log?

• Add a constant to both sides

• Simplify the logarithm

• Convert to an exponential equation

• Convert to a quadratic equation

In the exponential equation, what is the value of 10 raised to the second power?

• 20

• 10

• 100

• 1000

What operation is performed after writing the exponential equation to solve for x?

• Subtract 4 from both sides

• Divide by 10

• Cross-multiply

• Add x to both sides

What is the result of distributing 100 in the equation 100(x + 2)?

• 100x + 2

• 100x + 400

• 100x + 200

• 100x + 4

After simplifying, what is the equation before isolating x?

• 99x + 200 = 4

• 100x + 4 = 200

• x + 200 = 100

• 99x = 196

What is the final value of x after solving the equation?

• 196/99

• -196/99

• -99/196

• 99/196

Why is it important to check if the solution for x is valid?

• To ensure x is a positive number

• To confirm x is an integer

• To verify x satisfies the original logarithmic conditions

• To make sure x is less than zero

What condition must x satisfy in the original logarithmic equation?

• x must be greater than -2

• x must be equal to 0

• x must be less than -2

• x must be greater than 2