ln(x^2+3)-ln(x^2)=1

Lösung

ln (x^{2} + 3) - ln (x^{2}) = 1

x = \frac{3}{e - 1}, x = - \frac{3}{e - 1}

Dezimale

x = 1.32133 \dots, x = - 1.32133 \dots

Schritte zur Lösung

ln (x^{2} + 3) - ln (x^{2}) = 1

Füge

ln (x^{2})

zu beiden Seiten hinzu

ln (x^{2} + 3) - ln (x^{2}) + ln (x^{2}) = 1 + ln (x^{2})

Vereinfache

ln (x^{2} + 3) = 1 + ln (x^{2})

Wende die log Regel an

x^{2} + 3 = e x^{2}

Löse

x^{2} + 3 = e x^{2} : x = \frac{3}{e - 1}, x = - \frac{3}{e - 1}

x = \frac{3}{e - 1}, x = - \frac{3}{e - 1}

Überprüfe die Lösungen:

x = \frac{3}{e - 1}

Wahr

, x = - \frac{3}{e - 1}

Wahr

Die Lösungen sind

x = \frac{3}{e - 1}, x = - \frac{3}{e - 1}

ln (x) ln (x) = 1

lo g_{x} (3 x + 4) = lo g_{x} (4 x + 2)

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

- \frac{ln ( p )}{ln ( 7 )} - 4 = 0

1 + 2 ln (x) = 0