Wiki-Quellcode von Lösung Logarithmen und Exponentialgleichungen
Version 1.1 von Simone Hochrein am 2026/02/04 16:00
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| author | version | line-number | content |
|---|---|---|---|
 |
1.1 | 1 | (% class="abc" %) |
| 2 | 1. **Lösung zu 2.1:** | ||
| 3 | {{formula}} | ||
| 4 | \begin{aligned} | ||
| 5 | 49^{x} &= 343 \\ | ||
| 6 | (7^{2})^{x} &= 7^{3} \\ | ||
| 7 | 7^{2x} &= 7^{3} & \text{| Exponentenvergleich} \\ | ||
| 8 | 2x &= 3 \\ | ||
| 9 | x &= 1,5 | ||
| 10 | \end{aligned} | ||
| 11 | {{/formula}} | ||
| 12 | |||
| 13 | 1. **Lösung zu 2.2:** | ||
| 14 | {{formula}} | ||
| 15 | \begin{aligned} | ||
| 16 | 4^{0,6x+1,5} + 38 &= 550 & |- 38 \\ | ||
| 17 | 4^{0,6x+1,5} &= 512 \\ | ||
| 18 | (2^{2})^{0,6x+1,5} &= 2^{9} \\ | ||
| 19 | 2^{1,2x+3} &= 2^{9} & \text{| Exponentenvergleich} \\ | ||
| 20 | 1,2x + 3 &= 9 & |- 3 \\ | ||
| 21 | 1,2x &= 6 & |: 1,2 \\ | ||
| 22 | x &= 5 | ||
| 23 | \end{aligned} | ||
| 24 | {{/formula}} | ||
| 25 | |||
| 26 | 1. **Lösung zu 2.3:** | ||
| 27 | {{formula}} | ||
| 28 | \begin{aligned} | ||
| 29 | \log_{x}(7776) &= 5 & \text{| Definition des Logarithmus} \\ | ||
| 30 | x^{5} &= 7776 & |\sqrt[5]{\dots} \\ | ||
| 31 | x &= \sqrt[5]{7776} \\ | ||
| 32 | x &= 6 | ||
| 33 | \end{aligned} | ||
| 34 | {{/formula}} |