Wiki-Quellcode von Lösung Exponentialgleichungen (Logarithmieren)
Zuletzt geändert von akukin am 2025/08/11 15:31
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| author | version | line-number | content |
|---|---|---|---|
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8.1 | 1 | (% class="123" %) |
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9.1 | 2 | 1. {{formula}} e^x=3 \quad \mid ln( ) {{/formula}} |
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1.1 | 3 | {{formula}} ln(e^x)=ln(3) {{/formula}} |
| 4 | {{formula}} x=ln(3) {{/formula}} | ||
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3.2 | 5 | {{formula}}\mathbb{L}= \left\{ ln(3) \right\} {{/formula}} |
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7.1 | 6 | |
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9.1 | 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}} | ||
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1.1 | 10 | {{formula}} x=ln(6) {{/formula}} |
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4.1 | 11 | {{formula}}\mathbb{L}= \left\{ ln(6) \right\} {{/formula}} |
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7.1 | 12 | |
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9.1 | 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}} | ||
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1.3 | 16 | {{formula}} x=-2 \cdot ln(3) {{/formula}} |
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4.1 | 17 | {{formula}}\mathbb{L}= \left\{-2 \cdot ln(3) \right\} {{/formula}} |
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7.1 | 18 | |
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9.1 | 19 | 1. {{formula}} e^x=-5 \quad \mid ln( ) {{/formula}} |
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1.3 | 20 | {{formula}}x=ln(-5){{/formula}} |
| 21 | keine Lösung! | ||
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4.1 | 22 | {{formula}}\mathbb{L}= \left\{ \right\} {{/formula}} |
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7.1 | 23 | |
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9.1 | 24 | 1. {{formula}} 4\cdot 5^x=100 \quad \mid:4 {{/formula}} |
| 25 | {{formula}} 5^x=25 \quad \mid \text{Exponentenvergleich} {{/formula}} | ||
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4.2 | 26 | {{formula}} 5^x=5^2 {{/formula}} |
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5.1 | 27 | {{formula}} x=2 {{/formula}} |
| 28 | {{formula}}\mathbb{L}= \left\{ 2 \right\} {{/formula}} |