Wiki-Quellcode von Lösung Exponentialgleichungen lösen
Version 16.1 von Christoph Gommel am 2026/02/02 21:06
Verstecke letzte Bearbeiter
| author | version | line-number | content |
|---|---|---|---|
 |
4.1 | 1 | |
| 2 | a) | ||
| 3 | {{formula}} | ||
| |
3.1 | 4 | \begin{align*} |
| |
4.1 | 5 | 4\cdot 5^x+20=120 &&& \mid -20 \\ |
| 6 | 4\cdot 5^x=100 &&& \mid :4 \\ | ||
| |
5.1 | 7 | 5^x=25 &&& \\ |
| |
7.1 | 8 | 5^x=5^2 &&& \mid Koeffizientenvergleich \\ |
| |
5.1 | 9 | x=2 \\ |
| 10 | \mathbb{L}= \left\{ 2 \right\} | ||
| |
4.1 | 11 | \end{align*} |
| |
7.1 | 12 | {{/formula}} |
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5.1 | 13 | |
| 14 | b) | ||
| 15 | {{formula}} | ||
| 16 | \begin{align*} | ||
| 17 | 2\cdot (2^x+4)=8 &&& \mid :2 \\ | ||
| |
7.1 | 18 | 2^x+4=4 &&& \mid -4 \\ |
| 19 | 2^x=0 &&& \\ | ||
| 20 | \mathbb{L}= \left\{ \right\} | ||
| |
5.1 | 21 | \end{align*} |
| |
7.1 | 22 | {{/formula}} |
| 23 | |||
| 24 | c) | ||
| 25 | {{formula}} | ||
| 26 | \begin{align*} | ||
| 27 | 2\cdot 3^x=6 &&& \mid :2 \\ | ||
| 28 | 3^x=3 \\ | ||
| 29 | \mathbb{L}= \left\{ 1 \right\} | ||
| 30 | \end{align*} | ||
| 31 | {{/formula}} | ||
| |
8.1 | 32 | |
| 33 | d) | ||
| 34 | {{formula}} | ||
| 35 | \begin{align*} | ||
| |
16.1 | 36 | & 1+2^x=7 &&&& \mid -1 \\ |
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14.1 | 37 | & 2^x=6 \\ |
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13.1 | 38 | & x=log_2 6 \\ |
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15.1 | 39 | & \mathbb{L}= \left\{ log_2 6 \right\} |
| |
8.1 | 40 | \end{align*} |
| 41 | {{/formula}} |