Logarithmic Equations and Verification

The video tutorial explains how to solve a logarithmic equation with different bases by using the change of base formula. It demonstrates factoring out common terms and converting the logarithmic equation into an exponential form to find the approximate value of x. The solution is verified by substituting the value back into the original equation.

What is the initial problem presented in the video?

• Solving a quadratic equation

• Solving a logarithmic equation with different bases

• Finding the derivative of a function

• Integrating a polynomial function

What is the purpose of the change of base formula?

• To convert a logarithm to a different base

• To solve quadratic equations

• To integrate a polynomial function

• To find the derivative of a function

How is the change of base formula applied to log base 3 of X?

• log X * log 3

• log 3 * log X

• log 3 / log X

• log X / log 3

What common factor is identified in the equation?

• Natural log of 3

• Natural log of 5

• Natural log of X

• Natural log of 12

What operation is performed after factoring out the common factor?

• Addition

• Subtraction

• Multiplication

• Division

What is the base of the natural logarithm used in the conversion?

• Base 2

• Base 10

• Base 5

• Base e

What is the approximate value of X found in the solution?

• 2527.7277

• 3456.7890

• 1234.5678

• 9876.5432

What is the final step to verify the solution?

• Substitute the approximate value back into the original equation

• Change the base of the logarithm

• Recalculate the entire equation

• Use a different method to solve the equation

What should the sum on the left side of the equation be approximately equal to after verification?

• 10

• 13

• 11

• 12

What is the significance of verifying the solution?

• To find a new solution

• To change the base of the logarithm

• To simplify the equation further

• To ensure the solution is correct