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Zuletzt geändert von Holger Engels am 2025/03/13 07:51
Von Version 48.1
bearbeitet von Martin Rathgeb
am 2025/02/25 17:55
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Auf Version 31.1
bearbeitet von Martin Rathgeb
am 2025/02/25 13:46
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8 8  [[Kompetenzen.K4]] [[Kompetenzen.K6]] Ich kann die Lösungen einer Exponentialgleichung als Schnittstelle zweier Funktionen interpretieren
9 9  
10 10  Aufgaben:
11 -– Logarithmus: graphisches Ermitteln vs. Operator
12 -Lösen von Exponentialgleichungen:
13 -– Vokabelheft für Umkehroperationen
14 14  – Umkehrung der Rechenoperationen (Logarithmieren!) zzgl. Grundrechenarten
15 15  – Faktorisierung durch Ausklammern und Satz vom Nullprodukt zzgl. Grundrechenarten
16 16  – Substitution (abc-Formel, pq-Formel, Typ I) zzgl. Grundrechenarten
17 17  - Näherungslösungen
18 18  
19 -Gleichungen:
20 -x+y = e --> y = e - x
21 -x*y = e --> y = e / x
22 -e^y = x --> y = ln(x)
23 23  
24 -{{aufgabe id="Gleichungsformen besetzen" afb="I" kompetenzen="K5" quelle="Elke Hallmann, Martin Rathgeb, Dirk Tebbe" cc="BY-SA" zeit="5"}}
25 -Bilde für {{formula}} a, b, c \in \{2; 3; 4; \ldots; 16\} {{/formula}} möglichst viele Gleichungen der folgenden Typen:
26 -(% class="abc" %)
27 -1. {{formula}} c = a^b {{/formula}}
28 -1. {{formula}} c = \sqrt[a]{b} {{/formula}}
29 -1. {{formula}} c = \log_a(b) {{/formula}}
30 -{{/aufgabe}}
31 -
32 -{{aufgabe id="Logarithmus auswerten" afb="I" kompetenzen="K5" quelle="Niklas Wunder" cc="BY-SA" zeit="5"}}
33 -Ordne (ohne WTR) die Terme ihren Werten gemäß den Kästchem über dem Zahlenstrahl zu. Trage dafür die jeweiligen Buchstaben in die Kästchen ein.
34 -(% class="abc" %)
35 -1. {{formula}} \log_{10}(10) {{/formula}}
36 -1. {{formula}} \log_{100}(10) {{/formula}}
37 -1. {{formula}} \log_{11}(10) {{/formula}}
38 -1. {{formula}} \log_{10}(1000) {{/formula}}
39 -1. {{formula}} \log_{10}(5) {{/formula}}
40 -1. {{formula}} \log_{11}(1000) {{/formula}}
41 -1. {{formula}} \log_{10}(1) {{/formula}}
42 -1. {{formula}} \log_{100}(10) {{/formula}}
43 -1. {{formula}} \log_{10}(10) {{/formula}}
44 -
45 -[[image:Logarithmus.svg||width="400px"]]
46 -{{/aufgabe}}
47 -
48 48  {{aufgabe id="Exponentialgleichungen (Logarithmieren)" afb="I" kompetenzen="K5" quelle="Niklas Wunder" cc="BY-SA" zeit="5"}}
49 49  Bestimme die Lösungsmenge der folgenden Exponentialgleichungen:
50 50  (% class="abc" %)
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53 53  1. {{formula}} 2e^x-4=8 {{/formula}}
54 54  1. {{formula}} 2e^{-0.5x}=6{{/formula}}
55 55  1. {{formula}} e^x=-5 {{/formula}}
56 -1. {{formula}} 2e^x=e^{2x} {{/formula}}
57 -1. {{formula}} 2e^x-3=e^{2x} {{/formula}}
58 58  {{/aufgabe}}
59 59  
60 60  {{aufgabe id="Exponentialgleichungen" afb="I" kompetenzen="K5" quelle="Niklas Wunder" cc="BY-SA" zeit="5"}}
2^x und 8.svg
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1 -XWiki.martinrathgeb
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38 -
Logarithmus.svg
Author
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x^3 und 8.svg
Author
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1 -XWiki.martinrathgeb
Größe
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1 -6.7 KB
Inhalt
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