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Zuletzt geändert von Holger Engels am 2025/03/13 07:51
Von Version 97.1
bearbeitet von Dirk Tebbe
am 2025/02/26 14:16
Änderungskommentar: Neuen Anhang x^3und8.ggb hochladen
Auf Version 79.1
bearbeitet von Martin Rathgeb
am 2025/02/26 11:56
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54 54  |y|0|1|8|27
55 55  )))
56 56  1. zwei Graphen
57 -[[image:8und2^x.svg||width="200px"]]
58 -[[image:x^3 und 8.svg||width="200px"]]
59 59  {{/aufgabe}}
60 60  
61 61  {{aufgabe id="Logarithmen auswerten" afb="II" kompetenzen="K4,K5" quelle="Elke Hallmann, Martin Rathgeb, Dirk Tebbe" cc="BY-SA" zeit="10"}}
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86 86  {{formula}} c = a^b\:; \qquad c = \sqrt[a]{b}\:; \qquad c = \log_a(b)\:. {{/formula}}
87 87  {{/aufgabe}}
88 88  
89 -
90 -{{aufgabe id="Gleichungstypen einstudieren" afb="II" kompetenzen="K5" quelle="Elke Hallmann, Martin Rathgeb, Dirk Tebbe, Martina Wagner" cc="BY-SA" zeit="5"}}
91 -Bestimme die Lösung der folgenden Gleichungen:
92 -
93 -(% class="border slim " %)
94 -|Typ 1 Umkehroperationen|Typ 2 Ausklammern|Typ 3 Substitution
95 -|{{formula}}x^2 = 2{{/formula}}|{{formula}}x^2-2x = 0{{/formula}}|{{formula}}x^4-40x^2+144 = 0{{/formula}}
96 -|{{formula}}x^4 = e{{/formula}}|{{formula}}2x^e = x^{2e}{{/formula}}|{{formula}}x^{2x}+x^e+1 = 0{{/formula}}
97 -|{{formula}}e^x = e{{/formula}}|{{formula}}2e^x = e^{2x}{{/formula}}|2
98 -|{{formula}}f_4(x){{/formula}}|2|1
99 -{{/aufgabe}}
100 -
101 -Nenne eine passende Gleichung. Die Gleichung kann ich nach x auflösen, indem ich {{formula}} \ldots {{/formula}}
102 -(% class="abc" %)
103 -1. {{formula}} \ldots {{/formula}} die Terme auf beiden Seiten durch 5 dividiere und damit die Lösung {{formula}} x = \frac{2}{5} {{/formula}} erhalte.
104 -1. {{formula}} \ldots {{/formula}} von beiden Termen die 5-te Wurzel ziehe und damit die Lösung {{formula}} x = \sqrt[5]{2} {{/formula}} erhalte.
105 -1. {{formula}} \ldots {{/formula}} die Terme auf beiden Seiten zur Basis 5 logarithmiere und damit die Lösung {{formula}} x = \log_5(2) {{/formula}} erhalte.
106 -{{/aufgabe}}
107 -
108 -
109 109  {{aufgabe id="Exponentialgleichungen (Logarithmieren)" afb="I" kompetenzen="K5" quelle="Elke Hallmann, Martin Rathgeb, Dirk Tebbe" cc="BY-SA" zeit="15"}}
110 110  Bestimme die Lösungsmenge der Exponentialgleichung:
111 111  (% class="abc" %)
x^3und8.ggb
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2^x und 8.svg
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x^3 und 8.svg
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