log_{3}((11x+30)^4)=16

Lösung

lo g_{3} ((11 x + 30)^{4}) = 16

x = \frac{51}{11}, x = - \frac{111}{11}

Dezimale

x = 4.63636 \dots, x = - 10.09090 \dots

Schritte zur Lösung

lo g_{3} ((11 x + 30)^{4}) = 16

Wende Exponentenregel an:

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

(11 x + 30)^{4} = ((11 x + 30)^{2})^{2}

lo g_{3} (((11 x + 30)^{2})^{2}) = 16

Wende die log Regel an

(11 x + 30)^{2} = 6561

Löse

(11 x + 30)^{2} = 6561 : x = \frac{51}{11}, x = - \frac{111}{11}

x = \frac{51}{11}, x = - \frac{111}{11}

Überprüfe die Lösungen:

x = \frac{51}{11}

Wahr

, x = - \frac{111}{11}

Wahr

Die Lösungen sind

x = \frac{51}{11}, x = - \frac{111}{11}

lo g_{23} (5 x - 1) = 2

2 lo g_{10} (5 x) = 6

2 ln (n) = ln (n^{2})

lo g_{2} (x + 8) = \frac{2}{21}

lo g_{3} (2 x) = 6 + 2 lo g_{3} (x)