Logarithmengesetze

Hier die wichtigsten Logarithmusgesetze zum umformen: 1. Regel l o g b a x = x ⋅ l o g b a 2. Regel l o g b ( u ⋅ v ) = l o g b u + l o g b v 3. Regel l o g b ( u v ) = l o g b u – l o g b v MathType@MTEF@5@5@+= feaagGart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfgBPj MCPbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVC0dg9qqqrpepC 0xbbL8F4rqWrFfpeea0xe9Gq=Jc9qspeea0xb9as=JfrVkFHe9pgea 0dXdar=tb9fs0dXdab6hc9qr0=yr0=vqpWqaaeaabaGaaiaacaqabe aadaabauaaaOqaaiaaiodacaGGUaGaaeiiaiaabccaqaaaaaaaaaWd biaacckacaGGGcGaaiiOaiaacckacaGGGcGaamiBaiaad+gacaWGNb WdamaaBaaaleaapeGaamOyaaWdaeqaaOWaaeWaaeaadaWcaaqaaiaa dwhaaeaacaWG2baaaaGaayjkaiaawMcaa8qacaGGGcGaeyypa0Jaae iiaiaadYgacaWGVbGaam4za8aadaWgaaWcbaWdbiaadkgaa8aabeaa k8qacaWG1bGaaeiiaiaacobicaqGGaGaamiBaiaad+gacaWGNbWdam aaBaaaleaapeGaamOyaaWdaeqaaOWdbiaadAhaaaa@5C08@ Und natürlich einige Beispiele zu den jeweiligen Regeln: Beispiel zu 1: MathType@MTEF@5@5@+= feaagGart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfgBPj MCPbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2C G4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVC0dg9qqqrpepC 0xbbL8F4rqWrFfpeea0xe9Gq=Jc9qspeea0xb9as=JfrVkFHe9pgea 0dXdar=tb9fs0dXdab6hc9qr0=yr0=vqpWqaaeaabaGaaiaacaqabe aadaabauaaaOaa@3CAC@</annotation> l o g 8 6,6 x = x ⋅ l o g 8 6,6 Beispiel zu 2: l o g 2 ( 8 ⋅ 7 x ) = l o g 2 8 + l o g 2 7 x = 3 + x ⋅ l o g 2 7 Beispiel zu 3: ln ( x 3 ) = ln ( x ) − ln ( 3 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd