# HW5 - Section 5.1 1 4 3 Â 4 5 = 4 3 5 = 4 2 = 16 3 3 Â 3 6...

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Unformatted text preview: Section 5.1 1. 4- 3 Â· 4 5 = 4- 3+5 = 4 2 = 16 . 3- 3 Â· 3 6 = 3- 3+6 = 3 3 = 27 . 3. 9(9)- 1 / 2 = 9 Â· 9- 1 / 2 = 9 1- (1 / 2) = 9 1 / 2 = âˆš 9 = 3 . 5(5)- 1 / 2 = 5 Â· 5- 1 / 2 = 5 1- (1 / 2) = 5 1 / 2 = âˆš 5 . 5. (- 3) 4 (- 3) 5 (- 3) 8 = (- 3) 4 (- 3) 5 (- 3)- 8 = (- 3) 4+5- 8 = (- 3) 1 =- 3 . (2)- 4 (2) 6 (2)- 1 = (2)- 4 (2) 6 (2) 1 = (2)- 4+6+1 = (2) 3 = 8 . 7. 5 3 . 3 5- 1 . 6 5- . 3 = 5 3 . 3 5- 1 . 6 5 . 3 = 5 3 . 3- 1 . 6+0 . 3 = 5 2 = 25 . 4 2 . 7 4- 1 . 3 4- . 4 = 4 2 . 7 4- 1 . 3 4 . 4 = 4 2 . 7- 1 . 3+0 . 4 = 4 1 . 8 . 9. (64 x 9 ) 1 / 3 = (4 3 x 9 ) 1 / 3 = (4 3 ) 1 / 3 ( x 9 ) 1 / 3 = (4) 3 / 3 ( x ) 9 / 3 = 4 x 3 . (25 x 3 y 4 ) 1 / 2 = (5 2 x 3 y 4 ) 1 / 2 = (5 2 ) 1 / 2 ( x 3 ) 1 / 2 ( y 4 ) 1 / 2 = (5) 2 / 2 ( x ) 3 / 2 ( y ) 4 / 2 = 5 y 2 x 3 / 2 = 5 y 2 x âˆš x. 11. 6 a- 5 3 a- 3 = 2 a- 5 a 3 = 2 a- 5+3 = 2 a- 2 = 2 a 2 . 4 b- 4 12 b- 6 = b- 4 b 6 3 = b- 4+6 3 = b 2 3 . 13. (2 x 3 y 2 ) 3 = (2) 3 ( x 3 ) 3 ( y 2 ) 3 = (8)( x ) 3 Â· 3 ( y ) 2 Â· 3 = 8 x 9 y 6 . (4 x 2 y 2 z 3 ) 2 = (4) 2 ( x 2 ) 2 ( y 2 ) 2 ( z 3 ) 2 = (16)( x ) 2 Â· 2 ( y ) 2 Â· 2 ( z ) 3 Â· 2 = 16 x 4 y 4 z 6 . 15. 5 (2- 3 x- 3 y 2 ) 2 = 1 (2- 3 ) 2 ( x- 3 ) 2 ( y 2 ) 2 = 1 (2)- 3 Â· 2 ( x )- 3 Â· 2 ( y ) 2 Â· 2 = 1 (2)- 6 ( x )- 6 ( y ) 4 = 2 6 x 6 y 4 = 64 x 6 y 4 . ( x + y )( x- y ) ( x- y ) = ( x + y )( x- y ) 1 = x 2- y 2 . 17. 6 2 x = 6 4 ; since the bases are the same on each side of the equality, we equate the exponents and obtain: 2 x = 4 â†’ x = 2 . 19. 3 3 x- 4 = 3 5 ; since the bases are the same on each side of the equality, we equate the exponents and obtain: 3 x- 4 = 5 â†’ x = 3 . 21. (2 . 1) x +2 = (2 . 1) 5 ; since the bases are the same on each side of the equality, we equate the exponents and obtain: x + 2 = 5 â†’ x = 3 . 23. 8 x = 1 32 x- 2 (2 3 ) x = 1 2 5 x- 2 (2) 3 x = (2- 5 ) x- 2 (2) 3 x = (2)- 5( x- 2) = (2)- 5 x +10 . Since the bases are the same on each side of the equality, we equate the exponents and obtain: 3 x =- 5 x + 10 â†’ x = (10 / 8) = (5 / 4) . 25. 3 2 x- 12 Â· 3 x + 27 = 0 (3 x- 9)(3 x- 3) = 0 which implies that (3 x- 9) = 0 or (3 x- 3) = 0 . (3 x- 9) = (3 x- 3 2 ) = 0 â†’ 3 x = 3 2 â†’ x = 2 . (3 x- 3) = (3 x- 3 1 ) = 0 â†’ 3 x = 3 1 â†’ x = 1 . 41. 1982 â†’ t = 0 , R (0) = 26 . 3 e- . 016(0) = 26 . 3 e = 26 . 3(1) = 26 . 3 percent . 1986 â†’ t = 4 , R (4) = 26 . 3 e- . 016(4) = 26 . 3 e- . 064 = 26 . 3(0 . 9380) = 24 . 67 percent . 1994 â†’ t = 12 , R (12) = 26 . 3 e- . 016(12) = 26 . 3 e- . 192 = 26 . 3(0 . 8253) = 21 . 71 percent . 2000 â†’ t = 18 , R (12) = 26 . 3 e- . 016(18) = 26 . 3 e- . 2880 = 26 . 3(0 . 7498) = 19 . 72 percent . 43. No explanation required. 45. 2010 â†’ t = 6 , N (6) = 35 . 5 1+6 . 89 e- . 8674(6) = 35 . 5 1+6 . 89 e- 5 . 204 = 35 . 5 1+6 . 89(0 . 0055) = 34 . 20 million taxpayers. Section 5.2 17. 2 ln a + 3 ln b = ln a 2 + ln b 3 = ln( a 2 b 3 ) ....
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## This note was uploaded on 02/14/2012 for the course MAC 2233 taught by Professor Smith during the Spring '08 term at University of Florida.

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HW5 - Section 5.1 1 4 3 Â 4 5 = 4 3 5 = 4 2 = 16 3 3 Â 3 6...

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