Unterschiede
Hier werden die Unterschiede zwischen zwei Versionen angezeigt.
| home-harmening:mathematik:potenzen_und_wurzel [2025/10/27 17:47] – angelegt charmening | home-harmening:mathematik:potenzen_und_wurzel [2025/10/27 17:48] (aktuell) – charmening | ||
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| Zeile 1: | Zeile 1: | ||
| ====== Potenzen und Wurzel ====== | ====== Potenzen und Wurzel ====== | ||
| * $ (ab)^{\frac{1}{2}} = \sqrt{ab} = \sqrt{a} * \sqrt{b} $ | * $ (ab)^{\frac{1}{2}} = \sqrt{ab} = \sqrt{a} * \sqrt{b} $ | ||
| + | \\ | ||
| * log_{b}(x)=y => b^{y} = x | * log_{b}(x)=y => b^{y} = x | ||
| \\ | \\ | ||
| === Beispiele === | === Beispiele === | ||
| * $ \sqrt{50} = \sqrt{25*2} = 5 * \sqrt{2} $ | * $ \sqrt{50} = \sqrt{25*2} = 5 * \sqrt{2} $ | ||
| + | \\ | ||
| * $ \sqrt{12} * \sqrt{27} = \sqrt{12*27} = \sqrt{3+4+3+9} $ | * $ \sqrt{12} * \sqrt{27} = \sqrt{12*27} = \sqrt{3+4+3+9} $ | ||
| + | \\ | ||
| * $ \sqrt{16x^{4}} = 4*x^{2} $ | * $ \sqrt{16x^{4}} = 4*x^{2} $ | ||
| + | \\ | ||
| * $ \sqrt{x+3}=5 | ^2 $ \\ $ x+3=25 | -3 $ \\ $ x =22 $ | * $ \sqrt{x+3}=5 | ^2 $ \\ $ x+3=25 | -3 $ \\ $ x =22 $ | ||
| + | \\ | ||
| * $ log_{10}(1000)=3 $ | * $ log_{10}(1000)=3 $ | ||
| + | \\ | ||
| * $ log_{2}(16)+log_{2}(4)=4+2=6 $ \\ oder $ log_{2}(16*4) => log_{2}(64) => 2^{6} => 6 $ | * $ log_{2}(16)+log_{2}(4)=4+2=6 $ \\ oder $ log_{2}(16*4) => log_{2}(64) => 2^{6} => 6 $ | ||
| + | \\ | ||
| * $ log_{x}(64) = 3 => x^{3} = 64 => x=4 $ | * $ log_{x}(64) = 3 => x^{3} = 64 => x=4 $ | ||