1. Solving Exponential Equations

2. Lesson Objective Lesson Success Criteria To explain how to solve equations that contain exponents Can recognise an exponential equation Is familiar with the powers of basic whole numbers Can manipulate equations and expressions that contain exponents Can successfully solve exponential equations

3. What is an Exponent? All numbers can be written in index form a x a is called the base x is called the index, power or exponent A number such as 9, can be written as 9 1 or 3 2 or81 ½ These have different bases, and different exponents, but all represent the same number.

4. Laws of Exponents (recap)

5. Powers of whole numbers It is very useful to be familiar with the following powers. x2x2x 3x3x 4x4x 5x5x 01111 12345 2491625 382764125 41681256625 53224310243125

6. Solving Equations with Exponents To solve equations with exponents you need to get the base and exponent on each side of the equation equal. Examplex 3 = 64can be rewritten as x 3 = 4 3 i.e. x = 4 We ask ourselves what to the power of 3 is equal to 64? It has to be to the power of 3 as both sides of the equation must have the same base and exponent.

7. Solving Equations with Exponents What aboutq 4 = 256 q 4 = 4 4 q = 4 If you are not sure, then guess and check is the best method. All your answers will be integers for this year. Back to the above problem, couldn’t q = -4 also be answer?? i.e. (-4) 4 = 256therefore 2 answers, q = -4, +4 When there is an even exponent, you will always have two answers for the base, plus or minus the solution.

8. Solving Equations with Exponents

11. Another word problem. There is a story about an emperor who offered a reward to any man who would marry his daughter. He said he would give him one grain of rice for the first square of a cheese board, 2 grains for the second square, 4 grains for the third square and so on. The equation is R = 2 s R = number of grains of rice s = number of squares. For which square would he receive 16384 grains of rice?

12. Homework Solving Exponential Equations Ex W, X: Pages 70-72