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

Lösung

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

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

Dezimale

x = - 0.19967 \dots

Schritte zur Lösung

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

Wenn

f (x) = g (x),

dann

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

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

Vereinfache

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

x^{2} = 1 0^{2 x - 1}

Löse

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

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

Überprüfe die Lösungen:

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

Wahr

Deshalb ist die Lösung

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

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

lo g_{10} (x) (100) = 2

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

1.1635 = 0.6446 ln (x) - 0.5557

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