Logarithmic Equations and Solutions

The video tutorial explains how to solve a logarithmic equation using the property that if two logarithms with the same base are equal, their arguments must also be equal. The tutorial provides a step-by-step solution to the equation log base 4 of 6X equals log base 4 of 4x + 5, resulting in x = 2.5. The solution is verified by substituting back into the original equation, confirming the correctness of the solution.

What is the initial logarithmic equation given in the problem?

• log base 4 of 6X = log base 4 of (5x + 4)

• log base 5 of 6X = log base 5 of (4x + 5)

• log base 4 of 6X = log base 4 of (4x + 5)

• log base 5 of 6X = log base 5 of (5x + 4)

Which property of logarithms is used to equate the expressions inside the logs?

• Power Property

• Product Property

• One-to-One Property

• Quotient Property

What is the first step in solving the equation for x?

• Add 4X to both sides

• Subtract 4X from both sides

• Divide both sides by 4

• Multiply both sides by 4

After simplifying, what equation do we get before solving for x?

• 2x = 5

• x = 5

• 4x = 5

• 6x = 5

What is the value of x after solving the equation?

• x = 3

• x = 3.5

• x = 2.5

• x = 2

What is the purpose of substituting the solution back into the original equation?

• To find a new solution

• To change the base of the logarithm

• To verify the correctness of the solution

• To simplify the equation further

What is the simplified form of the left side of the equation after substitution?

• log base 4 of 12

• log base 4 of 10

• log base 4 of 15

• log base 4 of 20

What is the simplified form of the right side of the equation after substitution?

• log base 4 of 10

• log base 4 of 12

• log base 4 of 15

• log base 4 of 20

What does the final verification of the solution show?

• The solution is correct

• The solution needs adjustment

• The solution is incomplete

• The solution is incorrect

What is the final conclusion about the solution?

• The solution is partially correct

• The solution needs further verification

• The solution is correct and verified

• The solution is incorrect