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Zuletzt geändert von Holger Engels am 2025/03/13 07:51
Von Version 40.1
bearbeitet von Martin Rathgeb
am 2025/02/25 17:32
Änderungskommentar: Neues Bild x^3 und 8.png hochladen
Auf Version 62.1
bearbeitet von Martin Rathgeb
am 2025/02/25 20:35
Änderungskommentar: Es gibt keinen Kommentar für diese Version

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... ... @@ -21,15 +21,53 @@
21 21  x*y = e --> y = e / x
22 22  e^y = x --> y = ln(x)
23 23  
24 -{{aufgabe id="Logarithmus" afb="I" kompetenzen="K5" quelle="Elke Hallmann, Martin Rathgeb, Dirk Tebbe" cc="BY-SA" zeit="5"}}
24 +{{aufgabe id="Exponentialgleichungen lösen (Grund- vs Fehlvorstellungen)" afb="I" kompetenzen="K5" quelle="Elke Hallmann, Martin Rathgeb, Dirk Tebbe" cc="BY-SA" zeit="5"}}
25 +(% class="abc" %)
26 +1. (((Beurteile folgende Aussagen:
27 +
28 +1) Die Gleichung {{formula}} 5^x = 2 {{/formula}} kann ich nach x auflösen, indem ich durch 5 dividiere. Ich erhalte damit die Lösung {{formula}} x = \frac{2}{5} {{/formula}}.
29 +2) Die Gleichung {{formula}} 5^x = 2 {{/formula}} kann ich nach x auflösen, indem ich die 5-te Wurzel verwende. Ich erhalte damit die Lösung {{formula}} x = \sqrt[5]{2} {{/formula}}.}}}
30 +3) Fürs Auflösen nach x benötige ich eine neue Methode bzw. Operation.
31 +)))
32 +2. Umkehraufgaben: Gib Gleichungen an, die durch die in 1) bzw. die in 2) genannte Methode gelöst werden.
33 +{{/aufgabe}}
34 +
35 +{{aufgabe id="Exponentialgleichungen lösen (graphisch vs rechnerisch)" afb="I" kompetenzen="K5" quelle="Elke Hallmann, Martin Rathgeb, Dirk Tebbe" cc="BY-SA" zeit="5"}}
36 +(% class="abc" %)
37 +Bestimme die Lösung der Gleichung {{formula}} 2^x = 5 {{/formula}} graphisch und rechnerisch.
38 +{{/aufgabe}}
39 +
40 +{{aufgabe id="Darstellungen zuordnen" afb="I" kompetenzen="K5" quelle="Elke Hallmann, Martin Rathgeb, Dirk Tebbe" cc="BY-SA" zeit="5"}}
41 +Ordne zu!
42 +(% class="abc" %)
43 +1. vier Gleichungen
44 +1. zwei Tabellen
45 +1. zwei Graphen
46 +{{/aufgabe}}
47 +
48 +{{aufgabe id="Gleichungsformen besetzen" afb="I" kompetenzen="K5" quelle="Elke Hallmann, Martin Rathgeb, Dirk Tebbe" cc="BY-SA" zeit="5"}}
25 25  Bilde für {{formula}} a, b, c \in \{2; 3; 4; \ldots; 16\} {{/formula}} möglichst viele Gleichungen der folgenden Typen:
50 +{{formula}} c = a^b\:; \qquad c = \sqrt[a]{b}\:; \qquad c = \log_a(b)\:. {{/formula}}
51 +{{/aufgabe}}
52 +
53 +{{aufgabe id="Logarithmen auswerten" afb="II" kompetenzen="K5" quelle="Elke Hallmann, Martin Rathgeb, Dirk Tebbe" cc="BY-SA" zeit="10"}}
54 +Ordne (ohne WTR) die Terme ihren Werten gemäß den Kästchen über dem Zahlenstrahl zu. Trage dafür die jeweiligen Buchstaben in die Kästchen ein.
55 +
56 +[[image:Logarithmus.svg||width="600px"]]
57 +
26 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}}
59 +1. {{formula}} \log_{10}(10) {{/formula}}
60 +1. {{formula}} \log_{100}(10) {{/formula}}
61 +1. {{formula}} \log_{11}(10) {{/formula}}
62 +1. {{formula}} \log_{10}(1000) {{/formula}}
63 +1. {{formula}} \log_{10}(5) {{/formula}}
64 +1. {{formula}} \log_{11}(1000) {{/formula}}
65 +1. {{formula}} \log_{10}(1) {{/formula}}
66 +1. {{formula}} \log_{100}(10) {{/formula}}
67 +1. {{formula}} \log_{10}(10) {{/formula}}
30 30  {{/aufgabe}}
31 31  
32 -{{aufgabe id="Exponentialgleichungen (Logarithmieren)" afb="I" kompetenzen="K5" quelle="Niklas Wunder" cc="BY-SA" zeit="5"}}
70 +{{aufgabe id="Exponentialgleichungen (Logarithmieren)" afb="I" kompetenzen="K5" quelle="Niklas Wunder" cc="BY-SA" zeit="10"}}
33 33  Bestimme die Lösungsmenge der folgenden Exponentialgleichungen:
34 34  (% class="abc" %)
35 35  1. {{formula}} 4\cdot 0,5^x=100 {{/formula}}
... ... @@ -37,7 +37,17 @@
37 37  1. {{formula}} 2e^x-4=8 {{/formula}}
38 38  1. {{formula}} 2e^{-0.5x}=6{{/formula}}
39 39  1. {{formula}} e^x=-5 {{/formula}}
78 +{{/aufgabe}}
79 +
80 +{{aufgabe id="Exponentialgleichungen (Ausklammern, SVNP)" afb="II" kompetenzen="K5" quelle="Niklas Wunder" cc="BY-SA" zeit="5"}}
81 +Bestimme die Lösungsmenge der folgenden Exponentialgleichungen:
82 +(% class="abc" %)
40 40  1. {{formula}} 2e^x=e^{2x} {{/formula}}
84 +{{/aufgabe}}
85 +
86 +{{aufgabe id="Exponentialgleichungen (Substitution)" afb="III" kompetenzen="K5" quelle="Niklas Wunder" cc="BY-SA" zeit="5"}}
87 +Bestimme die Lösungsmenge der folgenden Exponentialgleichungen:
88 +(% class="abc" %)
41 41  1. {{formula}} 2e^x-3=e^{2x} {{/formula}}
42 42  {{/aufgabe}}
43 43  
2^x und 8.png
Author
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1 -XWiki.martinrathgeb
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1 -883.7 KB
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x^3 und 8.png
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1 -XWiki.martinrathgeb
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2^x und 8.svg
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38 +
Logarithmus.svg
Author
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1 +7.5 KB
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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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