2log_{10}(3-x)=1-x

Lösung

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

x = \frac{2 W _{- 1} ( - \frac{l n ( 10 )}{20} )}{ln ( 10 )} + 3, x = \frac{2 W _{0} ( - \frac{l n ( 10 )}{20} )}{ln ( 10 )} + 3

Dezimale

x = 0.06469 \dots, x = 2.88597 \dots

Schritte zur Lösung

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

Teile beide Seiten durch

2

lo g_{10} (3 - x) = \frac{1 - x}{2}

Wenn

f (x) = g (x),

dann

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

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

Vereinfache

1 0^{l o g_{10} (3 - x)} : 3 - x

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

Löse

3 - x = 1 0^{\frac{1 - x}{2}} : x = \frac{2 W _{- 1} ( - \frac{l n ( 10 )}{20} )}{ln ( 10 )} + 3, x = \frac{2 W _{0} ( - \frac{l n ( 10 )}{20} )}{ln ( 10 )} + 3

x = \frac{2 W _{- 1} ( - \frac{l n ( 10 )}{20} )}{ln ( 10 )} + 3, x = \frac{2 W _{0} ( - \frac{l n ( 10 )}{20} )}{ln ( 10 )} + 3

Überprüfe die Lösungen:

x = \frac{2 W _{- 1} ( - \frac{l n ( 10 )}{20} )}{ln ( 10 )} + 3

Wahr

, x = \frac{2 W _{0} ( - \frac{l n ( 10 )}{20} )}{ln ( 10 )} + 3

Wahr

Die Lösungen sind

x = \frac{2 W _{- 1} ( - \frac{l n ( 10 )}{20} )}{ln ( 10 )} + 3, x = \frac{2 W _{0} ( - \frac{l n ( 10 )}{20} )}{ln ( 10 )} + 3

lo g_{2} (4 x + 9) = 4

lo g_{2} (x) + lo g_{8} (x) = 8

lo g_{7} (7 x - 3) = lo g_{7} (5 x + 15)

so l v e f or x, ln (x) = 5 k

lo g_{10} (x^{2} - 21 x) = 1