Änderungen von Dokument Lösung Exponentialgleichungen (Logarithmieren)
Zuletzt geändert von akukin am 2025/08/11 15:31
Zusammenfassung
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Seiteneigenschaften (2 geändert, 0 hinzugefügt, 0 gelöscht)
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... ... @@ -1,24 +1,28 @@ 1 -(% class=" abc" %)2 -1. {{formula}} e^x=3 \quad \ left|ln( ) {{/formula}}1 +(% class="123" %) 2 +1. {{formula}} e^x=3 \quad \mid ln( ) {{/formula}} 3 3 {{formula}} ln(e^x)=ln(3) {{/formula}} 4 4 {{formula}} x=ln(3) {{/formula}} 5 5 {{formula}}\mathbb{L}= \left\{ ln(3) \right\} {{/formula}} 6 -1. {{formula}} 2e^x-4=8 \quad \left|+4{{/formula}} 7 -{{formula}} 2e^x=12 \quad \left|:2{{/formula}} 8 -{{formula}} e^x=6 \quad \left| ln( ) {{/formula}} 6 + 7 +1. {{formula}} 2e^x-4=8 \quad \mid +4{{/formula}} 8 +{{formula}} 2e^x=12 \quad \mid :2{{/formula}} 9 +{{formula}} e^x=6 \quad \mid ln( ) {{/formula}} 9 9 {{formula}} x=ln(6) {{/formula}} 10 10 {{formula}}\mathbb{L}= \left\{ ln(6) \right\} {{/formula}} 11 -1. {{formula}} 2e^{-0.5x}=6 \quad \left|:2 {{/formula}} 12 -{{formula}} e^{-0.5x}=3 \quad \left| ln( ) {{/formula}} 13 -{{formula}} -0.5x=ln(3) \quad \left|\cdot (-2) {{/formula}} 12 + 13 +1. {{formula}} 2e^{-0.5x}=6 \quad \mid :2 {{/formula}} 14 +{{formula}} e^{-0.5x}=3 \quad \mid ln( ) {{/formula}} 15 +{{formula}} -0.5x=ln(3) \quad \mid \cdot (-2) {{/formula}} 14 14 {{formula}} x=-2 \cdot ln(3) {{/formula}} 15 15 {{formula}}\mathbb{L}= \left\{-2 \cdot ln(3) \right\} {{/formula}} 16 -1. {{formula}} e^x=-5 \quad \left| ln( ) {{/formula}} 18 + 19 +1. {{formula}} e^x=-5 \quad \mid ln( ) {{/formula}} 17 17 {{formula}}x=ln(-5){{/formula}} 18 18 keine Lösung! 19 19 {{formula}}\mathbb{L}= \left\{ \right\} {{/formula}} 20 -1. {{formula}} 4\cdot 5^x=100 \quad \left|:4 {{/formula}} 21 -{{formula}} 5^x=25 \quad \left| \text{Exponentenvergleich} {{/formula}} 23 + 24 +1. {{formula}} 4\cdot 5^x=100 \quad \mid:4 {{/formula}} 25 +{{formula}} 5^x=25 \quad \mid \text{Exponentenvergleich} {{/formula}} 22 22 {{formula}} 5^x=5^2 {{/formula}} 23 23 {{formula}} x=2 {{/formula}} 24 24 {{formula}}\mathbb{L}= \left\{ 2 \right\} {{/formula}}