ln(y^2)=ln(y+3)+2

Lösung

ln (y^{2}) = ln (y + 3) + 2

y = \frac{e ^{2} + e ^{4} + 12 e ^{2}}{2}, y = \frac{e ^{2} - e ^{4} + 12 e ^{2}}{2}

Dezimale

y = 9.67923 \dots, y = - 2.29017 \dots

Schritte zur Lösung

ln (y^{2}) = ln (y + 3) + 2

Wende die log Regel an

y^{2} = (y + 3) e^{2}

Löse

y^{2} = (y + 3) e^{2} : y = \frac{e ^{2} + e ^{4} + 12 e ^{2}}{2}, y = \frac{e ^{2} - e ^{4} + 12 e ^{2}}{2}

y = \frac{e ^{2} + e ^{4} + 12 e ^{2}}{2}, y = \frac{e ^{2} - e ^{4} + 12 e ^{2}}{2}

Überprüfe die Lösungen:

y = \frac{e ^{2} + e ^{4} + 12 e ^{2}}{2}

Wahr

, y = \frac{e ^{2} - e ^{4} + 12 e ^{2}}{2}

Wahr

Die Lösungen sind

y = \frac{e ^{2} + e ^{4} + 12 e ^{2}}{2}, y = \frac{e ^{2} - e ^{4} + 12 e ^{2}}{2}

x^{2} ln (x) - 9 ln (x) = 0

so l v e f or x, ln (x) = z

lo g_{5} (x + 1) = 2 + lo g_{5} (3 x - 2)

ln ∣ x ∣ = ln (x^{2})

lo g_{4} (v) = 4