2log_{10}(x+3)=2x+3

Lösung

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

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

Dezimale

x = - 1.25926 \dots, x = - 2.96578 \dots

Schritte zur Lösung

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

Teile beide Seiten durch

2

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

Wenn

f (x) = g (x),

dann

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

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

Vereinfache

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

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

Löse

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

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

Überprüfe die Lösungen:

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

Wahr

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

Wahr

Die Lösungen sind

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

lo g_{10} (x) + lo g_{10} (x + 4) = - 1

lo g_{125} (x) - lo g_{5} (x) = - 2

20 \cdot lo g_{10} (x) = 100

lo g_{2} (x) \cdot lo g_{2} (x) = 9

lo g_{x} (121) = 2