### Home > CAAC > Chapter 12 > Lesson 12.4.4 > Problem 12-106

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 (*x*)^{a}=^{b}*x*, then^{ab}must equal . I can simplify this to become . Therefore must be *x*and when*x*= 10,.” Who used inductive reasoning? Who used deductive reasoning? For each person, explain how you know.

What is the difference between inductive and deductive reasoning?

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.