Solving Logarithmic Equations with One-to-One Property

The video tutorial explains how to solve logarithmic equations with logs on both sides. It begins by introducing the problem and discussing the method of condensing logarithms to simplify the equation. The one-to-one property is then explained, showing how it can be used to equate expressions when the logs have the same base. The tutorial proceeds with solving the equation step-by-step, demonstrating the application of these properties. Finally, the solution is verified, ensuring the values satisfy the original logarithmic expressions.

What is the first step in solving a logarithmic equation with logarithms on both sides?

• Add the logarithms together

• Condense the logarithms

• Subtract the logarithms

• Multiply the logarithms

What does the one-to-one property state?

• If log(x) = log(y), then x ≠ y

• If log(x) = log(y), then x > y

• If log(x) = log(y), then x = y

• If log(x) = log(y), then x < y

Which operation can be performed on both sides of an equation without changing its equality?

• Subtracting different numbers from each side

• Adding a different number to each side

• Multiplying both sides by different numbers

• Adding the same number to both sides

What happens when you take the square root of both sides of an equation?

• The equation becomes invalid

• The equality is maintained

• The equation becomes a polynomial

• The equation becomes a logarithm

If log(x) = log(2), what can be concluded about x?

• x < 2

• x = 2

• x ≠ 2

• x > 2

What can be done when you have log base 2 on both sides of an equation?

• Cancel the logs

• Subtract the logs

• Multiply the logs

• Add the logs together

What is the resulting equation after canceling out the logs in the given problem?

• 2x + 3 = x + 4

• 2x - 3 = x + 4

• 2x - 3 = x - 4

• 2x + 3 = x - 4

What is the value of x after solving the equation 2x - 3 = x + 4?

• x = 8

• x = 7

• x = 6

• x = 5

What should be done after finding the value of x to ensure it is correct?

• Ignore it

• Plug it back into the original logarithms

• Multiply it by 2

• Subtract it from 10

What is the final step in verifying the solution to the logarithmic equation?

• Check if the value of x results in negative logarithms

• Check if the value of x results in positive logarithms

• Check if the value of x is positive

• Check if the value of x is negative