2log_{10}(x+2)=x

Lösung

2 lo g_{10} (x + 2) = x

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

Dezimale

x = 0.93530 \dots, x = - 1.88597 \dots

Schritte zur Lösung

2 lo g_{10} (x + 2) = x

Teile beide Seiten durch

2

lo g_{10} (x + 2) = \frac{x}{2}

Wenn

f (x) = g (x),

dann

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

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

Vereinfache

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

x + 2 = 1 0^{\frac{x}{2}}

Löse

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

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

Überprüfe die Lösungen:

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

Wahr

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

Wahr

Die Lösungen sind

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

4 = 5 lo g_{10} (x) - lo g_{2} (x)

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

4 (lo g_{5} (x) + lo g_{x} (5)) = 10

so l v e f or x, y - 1 = ln (x)

ln (x) + ln (x^{2} + 1) = 8