NJC 2017 H2 Maths Exponential Logarithm and Modulus Functions and their Graphs Solutions

National Junior College Mathematics Department 2016 Exponential, Logarithmic and Modulus Functions and their Graphs Page 1 of 7 National Junior College 2016 – 2017 H2 Mathematics Revision: Exponential, Logarithmic and Modulus Functions and their Graphs Solutions to Practice Questions 1. 2a   23 2 3 or 2 3 3 2 3 33 1 xx x x x x x x x x x           2b   42 4 2 or 4 2 2 2 4 2 1 4 2 (rej.) xx x x x x x x x x                2c    2 2 2 6 5 notice here that must be positive 65 5 6 0 3 2 0 2 or 3 x x x xx xx xx x         

National Junior College Mathematics Department 2016 Exponential, Logarithmic and Modulus Functions and their Graphs Page 2 of 7 2d         2 2 2 2 2 22 2 6 6 5 notice here that must be negative 65 6 5 if 6 0 or 6 5 if 6 0 5 6 0 6 5 6 1 0 5 6 0 1 (rej.) or 6 6 1 0 6 (rej.) or 1 x x x x xx x x x x x x x x x x x x x x x x x x                                  3     22 2 4 3 2 2 32 521 x x x x x        4     622 662 2 2 6 6 2 12 2 2 2 12 6 2 2 12 2 2 12 4 3 12 2 3 12 4 3 12 23 3 2 94 9 4 32 2 32 3 3 9 2 3 2 r rr r r r r r r rr r r r r r r r r r r r r x rr x x x x r xx rx r rx                       3 12 3 3 12 3 39 3 r r r r xx            23 3 3 12 4 3 3 18 22 18 18 33 27 3rk r      

National Junior College Mathematics Department 2016 Exponential, Logarithmic and Modulus Functions and their Graphs Page 3 of 7 5a      2 1 2 1 3 9 3 1 3 3 3 1 3 13 01 4 1 0 3 1 1 0 11 or 3 33xx x x x y yy y y x y yy y x                  5b      2 2 3 10 0 5 2 0 5 or 2 2 5 2 2 (rej.) l 2 n5 ln 2 3 2 10 0xx xx y yy yy x y               6 3xyk   0 0, 2 23 k x k y    

National Junior College Mathematics Department 2016 Exponential, Logarithmic and Modulus Functions and their Graphs Page 4 of 7 7 ln ln ln ln ln ln ln ln e ln e e ln ln e x x x x y x e y xy x y xy        8 log log• log • log · ·log lol g1log log og aa b c a a a aa a ba b c c a bc   9a     lg 2 5 1 lg lg 2 5 lg10 lg lg10 2 5 10 85 5 8 xx x x x xx x x           9b 2 8 2 42 2 2 124 log log 12 log loglog 25 122 1.5 12 8 log 8 62 y y x y yy x x xy           9c  lg 3 lg lg 7 3log lg 7 3 7 37 63 0.5 xx x x x x xx x x              9d 6 2 2 2 1 22 6 2 2 2 1 1 1 2 22 8 24 22 4 2 2 1 23 1.5 y y y y y y y y y yy y y               

National Junior College Mathematics Department 2016 Exponential, Logarithmic and Modulus Functions and their Graphs Page 5 of 7 10a 3223 xyx y     21 2 1 or 2 1 21 3 2 2 1 3 2 2 1 4 4 3 1 (rej.) 11 x y x y x yx x x x x x xy y                   10b 2 3 1 19 3 29x xy y   3 3 or 3 3 19 3 19 3 3322 19 3 2 6 19 3 2 6 19 5 6 19 5