2log_{10}(x-1)=2x-5

Lösung

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

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

Dezimale

x = 2.74073 \dots, x = 1.03421 \dots

Schritte zur Lösung

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

Teile beide Seiten durch

2

lo g_{10} (x - 1) = \frac{2 x - 5}{2}

Wenn

f (x) = g (x),

dann

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

1 0^{l o g_{10} (x - 1)} = 1 0^{\frac{2 x - 5}{2}}

Vereinfache

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

x - 1 = 1 0^{\frac{2 x - 5}{2}}

Löse

x - 1 = 1 0^{\frac{2 x - 5}{2}} : x = - \frac{W _{- 1} ( - \frac{l n ( 10 )}{e ^{\frac{3 l n ( 10 )}{2}}} ) - ln ( 10 )}{ln ( 10 )}, x = - \frac{W _{0} ( - \frac{l n ( 10 )}{e ^{\frac{3 l n ( 10 )}{2}}} ) - ln ( 10 )}{ln ( 10 )}

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

Überprüfe die Lösungen:

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

Wahr

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

Wahr

Die Lösungen sind

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

lo g_{x} (8 x - 3) - lo g_{x} (4) = 2

2 lo g_{8} (x + 2) = lo g_{8} (2 x + 19)

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

lo g_{10} (6 x) - 3 = - 4

ln (x + 3) = ln (x) + ln (3)