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Zuletzt geändert von Holger Engels am 2025/03/13 07:51
Von Version 72.1
bearbeitet von Martin Rathgeb
am 2025/02/26 11:21
Änderungskommentar: Neues Bild Logarithmus.svg hochladen
Auf Version 75.1
bearbeitet von Martin Rathgeb
am 2025/02/26 11:33
Änderungskommentar: Es gibt keinen Kommentar für diese Version

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22 22  e^y = x --> y = ln(x)
23 23  
24 24  {{aufgabe id="Exponentialgleichungen lösen (Fehlvorstellungen)" afb="I" kompetenzen="K5" quelle="Martin Rathgeb" cc="BY-SA" zeit="5"}}
25 +Nenne eine passende Gleichung.
25 25  (% class="abc" %)
26 -1. (((Beurteile folgende Aussagen:
27 -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}}.
28 -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}}.
29 -3) Um die Gleichung {{formula}} 5^x = 2 {{/formula}} nach x aufzulösen, benötige ich eine neue Methode bzw. eine neue Operation.
30 -)))
31 -1. Umkehraufgabe: Gib für jede in a) falsche Methode eine passende Gleichung an.
27 +1. Die Gleichung kann ich nach x auflösen, indem ich durch 5 dividiere und damit die Lösung {{formula}} x = \frac{2}{5} {{/formula}} erhalte.
28 +1. Die Gleichung kann ich nach x auflösen, indem ich die 5-te Wurzel verwende und damit die Lösung {{formula}} x = \sqrt[5]{2} {{/formula}} erhalte.
29 +1. Um die Gleichung {{formula}} 5^x = 2 {{/formula}} nach x aufzulösen, benötige ich eine neue Methode bzw. eine neue Operation.
32 32  {{/aufgabe}}
33 33  
34 34  {{aufgabe id="Gleichungsformen instantiieren" afb="I" kompetenzen="K2,K5" quelle="Martin Rathgeb, Dirk Tebbe" cc="BY-SA" zeit="5"}}
... ... @@ -47,7 +47,7 @@
47 47  {{aufgabe id="Logarithmen auswerten" afb="II" kompetenzen="K4,K5" quelle="Elke Hallmann, Martin Rathgeb, Dirk Tebbe" cc="BY-SA" zeit="10"}}
48 48  Ordne (ohne WTR!) die Terme ihren Werten gemäß den Kästchen über dem Zahlenstrahl zu. Trage dafür die jeweiligen Buchstaben in die Kästchen ein.
49 49  
50 -[[image:Logarithmus.svg||width="600px"]]
48 +[[image:Logarithmus_neu.svg||width="600px"]]
51 51  
52 52  (% class="abc" %)
53 53  1. {{formula}} \log_{10}(10) {{/formula}}
... ... @@ -68,7 +68,8 @@
68 68  
69 69  {{aufgabe id="Exponentialgleichungen Lösbarkeit (graphisch vs rechnerisch)" afb="I" kompetenzen="K5" quelle="Martin Rathgeb" cc="BY-SA" zeit="6"}}
70 70  (% class="abc" %)
71 -Gegeben sind die beiden Gleichungen {{formula}} 2^x = y_0 {{/formula}} und {{formula}} x^2 = y_0 {{/formula}}. Untersuche ihre Lösbarkeit in Abhängigkeit von {{formula}} y_0 {{/formula}}.
69 +Gegeben sind die beiden Gleichungen {{formula}} x^2 = a {{/formula}} und {{formula}} 2^x = a {{/formula}} für {{formula}} a \in \mathbb{R} {{/formula}}. Untersuche ihre Lösbarkeit in Abhängigkeit von {{formula}} a {{/formula}}.
70 +{{formula}} c = a^b\:; \qquad c = \sqrt[a]{b}\:; \qquad c = \log_a(b)\:. {{/formula}}
72 72  {{/aufgabe}}
73 73  
74 74  {{aufgabe id="Exponentialgleichungen (Logarithmieren)" afb="I" kompetenzen="K5" quelle="Elke Hallmann, Martin Rathgeb, Dirk Tebbe" cc="BY-SA" zeit="15"}}
Logarithmus_neu.svg
Author
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1 +XWiki.martinrathgeb
Größe
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1 +7.5 KB
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