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12-106.
  1. Andrew and Charles were each asked to find the value of when x = 10. Their work is shown below. Homework Help ✎

    Andrew: “When I tried other values of x for a different problem, I found that , , and . So, I predict that must equal 10.”

    Charles: “Since (xa)b = xab, then must equal . I can simplify this to become . Therefore must be x and when x = 10, .”

    1. Who used inductive reasoning? Who used deductive reasoning? For each person, explain how you know.

    2. What is the difference between inductive and deductive reasoning?

    3. Without a calculator, find the value of when x = 312 and when x = 7344.

Andrew used inductive reasoning because he extended a pattern; Charles used deductive reasoning because he based his reasoning on properties of exponents.

What are the definitions of inductive and deductive?

Follow the reasoning of Andrew and Charles.