Arithmetik und Algebra: Aufgaben by L. Locher-Ernst

By L. Locher-Ernst

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A+b+c. 32. (bc-ad):(b+c-a-d). 33. 1: (b - a), (b - a): (a l - a b + 1), (a· - a b + 1): (- a' + a l b - 2 a + b). 34. 1: (1 - a). 35. (a - 1): a. 36. a: (1 + 4 a). 37. a. 38. 25. 39. 7. 40. 5. 41. 20. 42. 15. 43. 5. 44. bl : a (b + 1)1. 45. 9. 46. 2 a. b e a 47. a + b, e - a, e - b. 48. a + b, a + b, a + b. 49. b' -c' a' 50. 0, a, b, e. 51. 3, - 7. 52. 4, - 2. 53. 3, 5. 1 Gruppe I: 1. 2" (b - a) . 2. a 3. = q u -/ ' b q- = u - ~1 ' q r < u. 275,35 und 640,145. q- a-be a a e _ 1 ' 1 < e < b oder b be - ad 5.

A + x)+ - (a - x)+}+. 11. J[ 3 x I 12. [x + (9 Xl - 4 yI)+]+ 2 + (x 2 - 1)+] [3 x - (9 Xl2 - 4 yl)+ ]+1+ I . - [x _ (x 2 If~]-1 _ + [x - (x 213. x+(l+X2)+r 1 1)+] fUr X= 1)+]-1. ~ {(:)+-(:)+}. [x + (x2 _ Gruppe T. Logarithmen 1. Mit den Bezeichnungen 10g2 = a, 10g3 = b stelle man dar: logl2, 1 10g216, logl,5, 10g45, 10gO,375, 10gO,04, log 15 , log 360, 10g25920. 2. Umzuformen: 10g,la,r;;, 10g{al'laya}, 10 Va+b 10 {(a-b)+V ab \. y vu y g Viib' g a+b a-bJ 3. Man bestimme x aus: 2 logx = 310ga logx = 1 3 + 410gb - slogc, + b), = -2 log (a 4 logx 2 logx = -310ga, ~ log~, n 43 Obungsaufgaben, Gruppe U 1 + b) logx = T log (a log x = log a + ~ 1 - zlog(b (lOg a +~ + e) - 1 Z log(e + a), log a) .

11. J[ 3 x I 12. [x + (9 Xl - 4 yI)+]+ 2 + (x 2 - 1)+] [3 x - (9 Xl2 - 4 yl)+ ]+1+ I . - [x _ (x 2 If~]-1 _ + [x - (x 213. x+(l+X2)+r 1 1)+] fUr X= 1)+]-1. ~ {(:)+-(:)+}. [x + (x2 _ Gruppe T. Logarithmen 1. Mit den Bezeichnungen 10g2 = a, 10g3 = b stelle man dar: logl2, 1 10g216, logl,5, 10g45, 10gO,375, 10gO,04, log 15 , log 360, 10g25920. 2. Umzuformen: 10g,la,r;;, 10g{al'laya}, 10 Va+b 10 {(a-b)+V ab \. y vu y g Viib' g a+b a-bJ 3. Man bestimme x aus: 2 logx = 310ga logx = 1 3 + 410gb - slogc, + b), = -2 log (a 4 logx 2 logx = -310ga, ~ log~, n 43 Obungsaufgaben, Gruppe U 1 + b) logx = T log (a log x = log a + ~ 1 - zlog(b (lOg a +~ + e) - 1 Z log(e + a), log a) .

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