Mathematik verstehen 6, Schulbuch

28 Kompetenzcheck 1 .121 Kreuze die Gleichungen an, die für alle a, b * ℝ 0 + gelten! 2 a – 2 _ 5 3 – 4 = a 8 _ 5  a – 2 _ 3 · a 3 _ 4 = a – 1 _ 2  9 ___ 98a– 9 ___ 50a= 9 __ 8a  3 9 __ a 2 b· 3 9 ___ a 4 b 8 = a 2 · b 3  3 9 ___ 8a 6 b 5 = 2a 2 b · 3 9 _ b  1 .122 Kreuze die richtige(n) Aussage(n) an! log 2 4 = log 4 8  log 5 5 = log 6 6  log 5 0,2 = log 10 0,1  log 3 27 = log 6 216  log 9 3 = log 49 7  1 .123 Kreuze an, was für alle a, b * ℝ + \{1} und alle x, y * ℝ + gilt! a) a x = b x w a = b  b) log a x = log b x w a = b  x a = x b w a = b  log a x = log a y w x = y  a x = a y w x = y  log a x = b w log b x = a  x a = y a w x = y  log a (b · x) = b · log a x  (x a ) b = (x b ) a w a = b  log a (x b ) = b · log a x  1 .124 Ordne jeder Gleichung in der linken Tabelle die äquivalente Gleichung aus der rechten Tabelle zu (a, b, c * ℝ + \{1} und x * ℝ )! a) b) 1 .125 Kreuze die beiden richtigen Aussagen an (a * ℝ + ) ! a) lne = 0  b) e x = a w x = lna  ln 1 _ e = 0  e x + 1 = a w x = lna + 1.  lne 2 = 1  e 2x = a w x = 2 · lna  ln 1 _ e 2 = – 2  e 2(x + 1) = a w x = 1 _ 2 · lna – 1  ln1 = 0  2 · e 2x = a w x = 1 _ 4 · ln a _ 2  Ag-r 2 .1 Ag-r 2 .1 Ag-r 2 .1 Ag-r 2 .1 a = b · c x A x = log 10 a __ c · log 10 b a = b cx B x = 2 · log 10 a __ log 10 b a 2 = b x C x = 2 · log 10 b __ log 10 a D x = log 10 2 a _ b 3 __ log 10 c a b = c A a = log b c a c = b B c = log b a b a = c C b = log a c b c = a D c = log a b E b = log c a F a = log c b Ag-r 2 .1 Nur zu Prüfzwecken – Eigentum des Verlags öbv