Solve Logarithmic Equations with Logs on Both Sides

The video tutorial explains how to solve a logarithmic equation using the one-to-one property of logarithms. It begins by introducing the equation and the concept of the one-to-one property, which states that if two logarithms with the same base are equal, their arguments must also be equal. The tutorial then demonstrates solving the resulting linear equation using inverse operations, leading to the final solution. The video concludes by summarizing the steps and confirming the solution.

What does the one-to-one property of logarithms state?

• If two logarithms have the same base, their arguments must be equal.

• Logarithms with different bases can be equated.

• Logarithms are only defined for positive numbers.

• The base of a logarithm can be any positive number.

What is the first step in solving the equation log base 5 of (4X - 7) = log base 5 of (X + 5)?

• Subtract X from both sides.

• Multiply both sides by 5.

• Set the arguments of the logarithms equal to each other.

• Add 7 to both sides.

After equating the arguments of the logarithms, what type of equation do we get?

• Linear equation

• Polynomial equation

• Exponential equation

• Quadratic equation

What operation is used to isolate the variable X in the equation 3X = 12?

• Addition

• Subtraction

• Multiplication

• Division

What is the solution for X in the equation 3X = 12?

• X = 4

• X = 6

• X = 3

• X = 5