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

Lösung

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

x = - \frac{W _{- 1} ( - \frac{l n ( 10 )}{30} )}{ln ( 10 )}, x = - \frac{W _{0} ( - \frac{l n ( 10 )}{30} )}{ln ( 10 )}

Dezimale

x = 1.71015 \dots, x = 0.03623 \dots

Schritte zur Lösung

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

Wenn

f (x) = g (x),

dann

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

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

Vereinfache

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

3 x = 1 0^{x - 1}

Löse

3 x = 1 0^{x - 1} : x = - \frac{W _{- 1} ( - \frac{l n ( 10 )}{30} )}{ln ( 10 )}, x = - \frac{W _{0} ( - \frac{l n ( 10 )}{30} )}{ln ( 10 )}

x = - \frac{W _{- 1} ( - \frac{l n ( 10 )}{30} )}{ln ( 10 )}, x = - \frac{W _{0} ( - \frac{l n ( 10 )}{30} )}{ln ( 10 )}

Überprüfe die Lösungen:

x = - \frac{W _{- 1} ( - \frac{l n ( 10 )}{30} )}{ln ( 10 )}

Wahr

, x = - \frac{W _{0} ( - \frac{l n ( 10 )}{30} )}{ln ( 10 )}

Wahr

Die Lösungen sind

x = - \frac{W _{- 1} ( - \frac{l n ( 10 )}{30} )}{ln ( 10 )}, x = - \frac{W _{0} ( - \frac{l n ( 10 )}{30} )}{ln ( 10 )}

4 ln (3 x + 5) - 12 = 16

ln (2 x + 1) - 1 = ln (x - 2)

- lo g_{10} (x) = 3.9

9 \times x^{l o g_{3} (x)} = x^{3}

lo g_{10} (4 x) - lo g_{10} (12 + x) = 2