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Beliebt Algebra >

log_{5}(6-5x)=1-x

Lösung

lo g_{5} (6 - 5 x) = 1 - x

Lösung

x = \frac{W _{- 1} ( - \frac{l n ( 5 )}{5 e ^{\frac{l n ( 5 )}{5}}} )}{ln ( 5 )} + \frac{6}{5}, x = \frac{W _{0} ( - \frac{l n ( 5 )}{5 e ^{\frac{l n ( 5 )}{5}}} )}{ln ( 5 )} + \frac{6}{5}

+1

Dezimale

x = - 0.21621 \dots, x = 1

Schritte zur Lösung

lo g_{5} (6 - 5 x) = 1 - x

Wenn

f (x) = g (x),

dann

a^{f (x)} = a^{g (x)}

5^{l o g_{5} (6 - 5 x)} = 5^{1 - x}

Vereinfache

5^{l o g_{5} (6 - 5 x)} : 6 - 5 x

6 - 5 x = 5^{1 - x}

Löse

6 - 5 x = 5^{1 - x} : x = \frac{W _{- 1} ( - \frac{l n ( 5 )}{5 e ^{\frac{l n ( 5 )}{5}}} )}{ln ( 5 )} + \frac{6}{5}, x = \frac{W _{0} ( - \frac{l n ( 5 )}{5 e ^{\frac{l n ( 5 )}{5}}} )}{ln ( 5 )} + \frac{6}{5}

x = \frac{W _{- 1} ( - \frac{l n ( 5 )}{5 e ^{\frac{l n ( 5 )}{5}}} )}{ln ( 5 )} + \frac{6}{5}, x = \frac{W _{0} ( - \frac{l n ( 5 )}{5 e ^{\frac{l n ( 5 )}{5}}} )}{ln ( 5 )} + \frac{6}{5}

Überprüfe die Lösungen:

x = \frac{W _{- 1} ( - \frac{l n ( 5 )}{5 e ^{\frac{l n ( 5 )}{5}}} )}{ln ( 5 )} + \frac{6}{5}

Wahr

, x = \frac{W _{0} ( - \frac{l n ( 5 )}{5 e ^{\frac{l n ( 5 )}{5}}} )}{ln ( 5 )} + \frac{6}{5}

Wahr

Die Lösungen sind

x = \frac{W _{- 1} ( - \frac{l n ( 5 )}{5 e ^{\frac{l n ( 5 )}{5}}} )}{ln ( 5 )} + \frac{6}{5}, x = \frac{W _{0} ( - \frac{l n ( 5 )}{5 e ^{\frac{l n ( 5 )}{5}}} )}{ln ( 5 )} + \frac{6}{5}

Graph

Beliebte Beispiele

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