Änderungen von Dokument BPE 4.5 Logarithmus und Exponentialgleichungen
Zuletzt geändert von Holger Engels am 2025/03/13 07:51
Von Version 23.1
bearbeitet von Niklas Wunder
am 2024/12/18 16:07
am 2024/12/18 16:07
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Auf Version 44.1
bearbeitet von Martin Rathgeb
am 2025/02/25 17:40
am 2025/02/25 17:40
Änderungskommentar:
Neues Bild x^3 und 8.svg hochladen
Zusammenfassung
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... ... @@ -1,1 +1,1 @@ 1 -XWiki. niklaswunder1 +XWiki.martinrathgeb - Inhalt
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... ... @@ -1,9 +1,5 @@ 1 -{{box cssClass="floatinginfobox" title="**Contents**"}} 2 -{{toc start=2 depth=2 /}} 3 -{{/box}} 1 +{{seiteninhalt/}} 4 4 5 -=== Kompetenzen === 6 - 7 7 [[Kompetenzen.K5]] Ich kann Logarithmus nutzen, um eine Exponentialgleichung zu lösen 8 8 [[Kompetenzen.K5]] Ich kann eine geeignete Strategie wählen, um eine gegebene Exponentialgleichung zu lösen 9 9 [[Kompetenzen.K1]] Ich kann die Wahl einer Lösungsstrategie für eine Exponentialgleichung begründen ... ... @@ -11,10 +11,43 @@ 11 11 [[Kompetenzen.K4]] [[Kompetenzen.K6]] Ich kann die Lösungen einer Exponentialgleichung als Nullstelle interpretieren 12 12 [[Kompetenzen.K4]] [[Kompetenzen.K6]] Ich kann die Lösungen einer Exponentialgleichung als Schnittstelle zweier Funktionen interpretieren 13 13 10 +Aufgaben: 11 +– Logarithmus: graphisches Ermitteln vs. Operator 12 +Lösen von Exponentialgleichungen: 13 +– Vokabelheft für Umkehroperationen 14 +– Umkehrung der Rechenoperationen (Logarithmieren!) zzgl. Grundrechenarten 15 +– Faktorisierung durch Ausklammern und Satz vom Nullprodukt zzgl. Grundrechenarten 16 +– Substitution (abc-Formel, pq-Formel, Typ I) zzgl. Grundrechenarten 17 +- Näherungslösungen 14 14 15 -{{aufgabe id="Exponentialgleichungen" afb="I" kompetenzen="K1-K6" quelle="Niklas Wunder" cc="BY-SA" zeit="5"}} 19 +Gleichungen: 20 +x+y = e --> y = e - x 21 +x*y = e --> y = e / x 22 +e^y = x --> y = ln(x) 23 + 24 +{{aufgabe id="Logarithmus" 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="Exponentialgleichungen (Logarithmieren)" afb="I" kompetenzen="K5" quelle="Niklas Wunder" cc="BY-SA" zeit="5"}} 33 +Bestimme die Lösungsmenge der folgenden Exponentialgleichungen: 34 +(% class="abc" %) 35 +1. {{formula}} 4\cdot 0,5^x=100 {{/formula}} 36 +1. {{formula}} e^x=3 {{/formula}} 37 +1. {{formula}} 2e^x-4=8 {{/formula}} 38 +1. {{formula}} 2e^{-0.5x}=6{{/formula}} 39 +1. {{formula}} e^x=-5 {{/formula}} 40 +1. {{formula}} 2e^x=e^{2x} {{/formula}} 41 +1. {{formula}} 2e^x-3=e^{2x} {{/formula}} 42 +{{/aufgabe}} 43 + 44 +{{aufgabe id="Exponentialgleichungen" afb="I" kompetenzen="K5" quelle="Niklas Wunder" cc="BY-SA" zeit="5"}} 16 16 Bestimme die Lösungsmenge der folgenden Exponentialgleichungen 17 -(% style="list-style:alphastyle" %)46 +(% class="abc" %) 18 18 1. {{formula}} 3^{x+1}=81 {{/formula}} 19 19 1. {{formula}} 5^{2x}=25^{2x+2} {{/formula}} 20 20 1. {{formula}} 10^{x}=500{{/formula}} ... ... @@ -21,12 +21,15 @@ 21 21 1. {{formula}} 2^{x+3}=4^{x-1} {{/formula}} 22 22 {{/aufgabe}} 23 23 24 -{{aufgabe id="Exponentialgleichungen graphisch" afb="II" kompetenzen="K4" quelle="Niklas Wunder" cc="BY-SA" zeit="5"}} 25 -Löse mit Hilfe der nebenstehenden Abbildung folgende Exponentialgleichungen näherungsweise. 26 -(% style="list-style:alphastyle" %)53 +{{aufgabe id="Exponentialgleichungen graphisch" afb="II" kompetenzen="K4,K6" quelle="Niklas Wunder" cc="BY-SA" zeit="5"}} 54 +Löse mit Hilfe der nebenstehenden Abbildung folgende Exponentialgleichungen näherungsweise. Hinweis: Ordne die linke und die rechte Seite der jeweiligen Gleichung passend den Funktionsgraphen zu. 55 +(% class="abc" %) 27 27 a) {{formula}} 2^x=(\frac{3}{4})^x+2 {{/formula}} 28 28 b) {{formula}} 7-e^{x-3}=(\frac{3}{4})^x+2 {{/formula}} 29 29 c) {{formula}} 2^x=1{,}5^{x+2}-0{,}5 {{/formula}} 30 30 d) {{formula}} 7-e^{x-3}=4-\frac{1}{2}\,x {{/formula}} 60 + 31 31 [[image:ExpGlei.svg]] 32 32 {{/aufgabe}} 63 + 64 +{{seitenreflexion/}}
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... ... @@ -1,0 +1,1 @@ 1 +XWiki.martinrathgeb - Größe
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