2log_{10}(9-2x)=(3-x)

Lösung

2 lo g_{10} (9 - 2 x) = (3 - x)

x = \frac{2 W _{- 1} ( - \frac{l n ( 10 )}{4 e ^{\frac{3 l n ( 10 )}{4}}} )}{ln ( 10 )} + \frac{9}{2}, x = \frac{2 W _{0} ( - \frac{l n ( 10 )}{4 e ^{\frac{3 l n ( 10 )}{4}}} )}{ln ( 10 )} + \frac{9}{2}

Dezimale

x = 1.42116 \dots, x = 4.40026 \dots

Schritte zur Lösung

2 lo g_{10} (9 - 2 x) = (3 - x)

Teile beide Seiten durch

2

lo g_{10} (9 - 2 x) = \frac{3 - x}{2}

Wenn

f (x) = g (x),

dann

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

1 0^{l o g_{10} (9 - 2 x)} = 1 0^{\frac{3 - x}{2}}

Vereinfache

1 0^{l o g_{10} (9 - 2 x)} : 9 - 2 x

9 - 2 x = 1 0^{\frac{3 - x}{2}}

Löse

9 - 2 x = 1 0^{\frac{3 - x}{2}} : x = \frac{2 W _{- 1} ( - \frac{l n ( 10 )}{4 e ^{\frac{3 l n ( 10 )}{4}}} )}{ln ( 10 )} + \frac{9}{2}, x = \frac{2 W _{0} ( - \frac{l n ( 10 )}{4 e ^{\frac{3 l n ( 10 )}{4}}} )}{ln ( 10 )} + \frac{9}{2}

x = \frac{2 W _{- 1} ( - \frac{l n ( 10 )}{4 e ^{\frac{3 l n ( 10 )}{4}}} )}{ln ( 10 )} + \frac{9}{2}, x = \frac{2 W _{0} ( - \frac{l n ( 10 )}{4 e ^{\frac{3 l n ( 10 )}{4}}} )}{ln ( 10 )} + \frac{9}{2}

Überprüfe die Lösungen:

x = \frac{2 W _{- 1} ( - \frac{l n ( 10 )}{4 e ^{\frac{3 l n ( 10 )}{4}}} )}{ln ( 10 )} + \frac{9}{2}

Wahr

, x = \frac{2 W _{0} ( - \frac{l n ( 10 )}{4 e ^{\frac{3 l n ( 10 )}{4}}} )}{ln ( 10 )} + \frac{9}{2}

Wahr

Die Lösungen sind

x = \frac{2 W _{- 1} ( - \frac{l n ( 10 )}{4 e ^{\frac{3 l n ( 10 )}{4}}} )}{ln ( 10 )} + \frac{9}{2}, x = \frac{2 W _{0} ( - \frac{l n ( 10 )}{4 e ^{\frac{3 l n ( 10 )}{4}}} )}{ln ( 10 )} + \frac{9}{2}

lo g_{10} (5 x + 1) = 2 + lo g_{10} (2 x - 3)

4 lo g_{2} (2 x) = 36

lo g_{10} (n) = - 0.35

lo g_{3} (x) + lo g_{3} (2 x + 1) = 1

lo g_{2} (x) = lo g_{4} (x^{2} + 2 x - 1)