Solving Logarithmic Equations: Key Techniques and Examples

The video tutorial demonstrates solving a logarithmic equation by first rewriting the equation using logarithmic properties, then solving for the variable, and finally verifying the solution. The example involves solving log base 7 of (X+4) minus log base 7 of (X-4) equals log base 7 of 5. The process includes setting the arguments of the logarithms equal, simplifying, and checking the solution to ensure it satisfies the original equation.

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

• 7

• 10

• X

• 5

What operation is performed when combining the two logarithmic expressions?

• Addition

• Subtraction

• Multiplication

• Division

What is the result of combining the logarithmic expressions?

• log base 7 of (X+4) * (X-4)

• log base 7 of (X+4) + (X-4)

• log base 7 of (X+4) / (X-4)

• log base 7 of (X+4) - (X-4)

What does the equation simplify to before solving for X?

• X + 4 = 5(X - 4)

• (X + 4) / (X - 4) = 5

• X - 4 = 5(X + 4)

• (X - 4) / (X + 4) = 5

What value of X solves the equation?

• 8

• 5

• 6

• 7

After solving, what is the equivalent expression for the left side of the equation?

• 5X - 20

• 24 = 4X

• X - 4

• X + 4

What mathematical operation is used to isolate X in the final steps?

• Multiplication

• Division

• Subtraction

• Addition

How do you check the solution's validity?

• Estimate the result

• Substitute X in the original equation

• Graph the equation

• Use a calculator

What is the final step in solving the logarithmic equation?

• Combine the logarithms

• Multiply both sides by X

• Check the solution

• Solve for X

What is the value of the logarithm when X is substituted back into the equation?

• log base 7 of 10

• log base 7 of 6

• log base 7 of 5

• log base 7 of 2