Week 4 Exponential equations for Math.pptx

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1. Solving Equations with Indices

2. Law of Indices Backwards Solve   The ‘thinking backwards’ method If I had some number to the power of , what would I do to it? Find the 4 th root then cube it. So going backwards from 27: Cube root: 3 Raise to the power of 4: 81   ? The ‘cancelling the power’ method. What power should I raise both sides of the equation to ‘cancel’ the power?   ? This part of the topic is a bit more Further Mathsey …

3. Further Examples Solve     ? Solve     ?

4. ? Test Your Understanding Solve   Solve       ?

5. Exercise 4 If , find . Solve   1 2 3 Questions on provided worksheet. [AQA FM June 2012 Paper 1] and . Calculate the value of   ? ? ?

6. Exercise 4 [AQA FM June 2013 Paper 1] Solve , writing your answer as a proper fraction.   ? 4 5 Questions on provided worksheet. [June 2013 Paper 2] . Write in terms of and . Give your answer in its simplest form.   ?

7. Exercise 4 [AQA FM Set 1 Paper 2] Given that and . Write in terms of . (b) Write in terms of and .   ? ? ? 6 7 Questions on provided worksheet. [AQA FM Set 3 Paper 1] and . Work out the value of .  

8. Exercise 4 [AQA FM Set 1 Paper 2] You are given that and . (c) Write in terms of .   ? 7 Questions on provided worksheet. (d) Write in terms of and .   ?

9. Power unknown What do you notice about all of the numbers: They’re all powers of 2! We could replace the numbers with , and so that we have a consistent base.   ?

10. Exponential Equations

11. Solving Exponential Equations Property of Equality for Exponential Equations Two powers with the same positive base b , where , are equal if and only if their exponents are equal. If , then . If and , then if and only if .  

12. Solving Exponential Equations with the Same Base Solve each equation   Since the bases are the same the exponents must equal each other.     Since the bases are the same the exponents must equal each other. Since the bases are the same the exponents must equal each other.

13. Solving Exponential Equations with the Same Base Solve each equation   Since the bases are the same the exponents must equal each other.     Since the bases are the same the exponents must equal each other. Since the bases are the same the exponents must equal each other.

14. You Try!! Solve each equation   1   1  

15. Solving Exponential Equations with Unlike Bases To solve some exponential equations, you must first rewrite each side of the equation using the same base.   Since the bases are not the same can you write 125 as some power of 5?   Since the bases are not the same can you write 4 as some power of 2?   Since the bases are not the same can you write 9 and 27 as the power of the same number? Powers of 3!

16. You Try!! Solve each equation      

17. Solving Exponential Equations with Unlike Bases To solve some exponential equations, you must first rewrite each side of the equation using the same base.   Since the bases are not the same can you write and 4 as the power of the same number? Powers of 2!     Since the bases are not the same can you write 4 and as the power of the same number? Powers of 4!  

18. You Try!! Solve the equation          

19. Let’s Review If the bases are already the same, equate the exponents. Then solve for x . If the bases are not the same think about what number raised to a power will equal the original base. Change both bases to the same base. Then equate the exponents. Then solve for the unknown.

20. When the power is unknown Solve     ? ? ? Solve     If , determine .   ? 1 2 3 First convert everything to powers of 2… ? First convert everything to powers of 2.

21. Test Your Understanding If , find . Solve   ? ? 1 2

22. Review 1 6 Write as a single power of : [Edexcel GCSE(9-1) Nov 2017 2F Q21c, Nov 2017 2H Q6c Edited]  can be written in the form  Express   in terms of   and  . Solve for :   [Edexcel GCSE(9-1) June 2017 2H Q18] Work out the exact value of  . [Edexcel IGCSE Jan2017-4H Q16d] Work out the exact value of  . Solve   2 3 4 5 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? a b c d e f g a b c d e