ln(x^4)+ln(x^2)=2

Lösung

ln (x^{4}) + ln (x^{2}) = 2

x = e^{\frac{2}{3}}, x = - e^{\frac{2}{3}}

Dezimale

x = 1.39561 \dots, x = - 1.39561 \dots

Schritte zur Lösung

ln (x^{4}) + ln (x^{2}) = 2

Wende Exponentenregel an:

a^{2 \cdot n} = (a^{2})^{n}

x^{4} = (x^{2})^{2}

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

Wende die log Regel an

x^{2} = e^{\frac{2}{3}}

Löse

x^{2} = e^{\frac{2}{3}} : x = e^{\frac{2}{3}}, x = - e^{\frac{2}{3}}

x = e^{\frac{2}{3}}, x = - e^{\frac{2}{3}}

Überprüfe die Lösungen:

x = e^{\frac{2}{3}}

Wahr

, x = - e^{\frac{2}{3}}

Wahr

Die Lösungen sind

x = e^{\frac{2}{3}}, x = - e^{\frac{2}{3}}

2 ln (x - 2) = ln (x)

lo g_{6} (lo g_{4} (x)) = 0

4 lo g_{10} (n) = n

so l v e f or x, ln (y - x^{2}) = 2

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