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chapter 4 - Chapter 4 Exercises 4.1 x 2x 2x 1 4 =(2 = 2 3 x...

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161 Chapter 4 Exercises 4.1 1. 4 x = (2 2 ) x = 2 2 x , 1/ 2 (1/ 2) ( 3) (3 ) 3 x x x = = , 1 9 x = (9 1 ) x = ((3 2 ) 1 ) x = 3 2 x 2. 27 x = (3 3 ) x = 3 3 x , 1/ 3 (1/ 3) 3 ( 2) (2 ) 2 x x x = = , 1 8 x = (8 1 ) x = ((2 3 ) 1 ) x = 2 3 x 3. 8 2 x /3 = (2 3 ) 2 x /3 = 2 3(2 x /3) = 2 2 x , 9 3 x / 2 = (3 2 ) 3 x /2 = 3 2(3 x /2) = 3 3 x , 16 3 x / 4 = (2 4 ) 3 x / 4 = 2 4( 3 x / 4) = 2 3 x 4. 9 x /2 = (3 2 ) x /2 = 3 2( x /2) = 3 x , 8 4 x /3 = (2 3 ) 4 x / 3 = 2 3(4 x /3) = 2 4 x , 27 2 x /3 = (3 3 ) 2 x /3 = 3 3( 2 x /3) = 3 2 x 5. 1 4 2 x = (4 1 ) 2 x = ((2 2 ) 1 ) 2 x = 2 4 x , 1 8 3 x = (8 1 ) 3 x = ((2 3 ) 1 ) 3 x = 2 9 x , 1 81 x /2 = (81 1 ) x / 2 = ((3 4 ) 1 ) x /2 = 3 2 x 6. 1 9 2 x = (9 1 ) 2 x = ((3 2 ) 1 ) 2 x = 3 4 x , 1 27 x /3 = (27 1 ) x /3 = ((3 3 ) 1 ) x /3 = 3 3( x /3) = 3 x 1 16 x /2 = (16 1 ) x /2 = ((2 4 ) 1 ) x /2 = 2 4( x /2) = 2 2 x 7. 6 x 3 x = (2 3) x 3 x = 2 x (3 x 3 x ) = 2 x (3 x x ) = 2 x , 15 x 5 x = (3 5) x 5 x = 3 x 5 x 5 x = 3 x , 12 x 2 2 x = (3 4) x 2 2 x = 3 x 4 x 2 2 x = 3 x (2 2 ) x 2 2 x = 3 x 8. 7 x 14 x = 7 x (7 2) x = 7 x 7 x 2 x = 7 x + x 2 x = 2 x 2 x 6 x = 2 (2 3) x = 2 x 2 x 3 x = 1 3 x = 3 x 3 2 x 18 x = 3 2 x 9 x 2 x = 3 2 x 3 2 x 2 x = 1 2 x = 2 x 9. 3 4 x 3 2 x = 3 4 x 3 2 x = 3 4 x 2 x = 3 2 x , 2 5 x + 1 2 2 x = 2 5 x + 1 2 1 x = 2 5 x + 1 2 (1 x ) = 2 5 x + 1 (1 x ) = 2 6 x , 9 x 27 x /3 = (3 2 ) x (3 3 ) x /3 = 3 2 x 3 x = 3 2 x 3 x = 3 2 x + x = 3 x 10. 2 x 6 x = 2 x (2 3) x = 2 x 2 x 3 x = 1 3 x = 3 x , 3 5 x 3 2 x = 3 5 x 3 2 x = 3 5 x + 2 x = 3 3 x , 16 x 8 x = (2 4 ) x (2 3 ) x = 2 4 x 2 3 x = 2 4 x + 2 x = 2 7 x 11. 2 3 x 2 5 x / 2 = 2 3 x (5 x /2) = 2 (6 x /2) (5 x /2) = 2 x / 2 , 3 2 x 1 3 2 x / 3 = 3 2 x (3 1 ) 2 x /3 = 3 2 x 3 2 x /3 = 3 (6 x /3) (2 x /3) = 3 4 x /3 = 3 (4/3) x 12. 2 5 x /4 1 2 x = 2 5 x /4 (2 1 ) x = 2 5 x / 4 2 4 x /4 = 2 (5 x /4) (4 x / 4) = 2 x /4 , 3 2 x 3 5 x /2 = 3 4 x /2 3 5 x /2 = 3 ( 4 x /2) + (5 x / 2) = 3 x /2 13. (2 3 x 2 2 x ) 2/5 = (2 3 x 2 x ) 2/5 = (2 5 x ) 2/ 5 = 2 2 x , (9 1/ 2 9 4 ) x / 9 = ((3 2 ) 1/2 (3 2 ) 4 ) x /9 = (3 1 3 8 ) x /9 = (3 1 + 8 ) x / 9 = (3 9 ) x /9 = 3 x 14. (3 x 3 x /5 ) 5 = 3 5 x 3 ( x /5)5 = 3 5 x 3 x = 3 5 x + x = 3 4 x , (16 1/4 16 3/4 ) 3 x = ((2 4 ) 1/ 4 (2 4 ) 3/4 ) 3 x = (2 1 2 3 ) 3 x = (2 1 3 )3 x = (2 2 ) 3 x = 2 6 x
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