Module 6: Exponents and Logarithms

 

In Self-Check 1 you practised changing the base of a power. In Try This 3 you will try to use this skill to solve exponential equations.

 

Try This 3

 

Complete the following questions to solve the equation 42x = 83x−2.

  1. How can you write 4 and 8 as powers with the same base?
  2. Write 42x as a power with the base you chose in question 1. What exponent law did you use to simplify the expression?
  3. Write 83x−2 as a power with the base you chose in question 1. What exponent law did you use to simplify the expression?
  4. Equate your answers from questions 2 and 3. Since both sides of the equation are single powers with the same base, the exponents must be equal. Set the exponents equal to each other and solve for x.
  5. Check if your answer is correct.
  6. Use a graphical method to solve the equation 42x = 83x−2. Describe the process you used.

course folder Save your responses in your course folder.

You can check your answer by substituting the value of x into the original equation and then determining if the left side equals the right side of the equation.
Did you try 2?