7^{x^2-x-2}=3^{x+2}

Lösung

7^{x^{2} - x - 2} = 3^{x + 2}

x = \frac{ln ( 21 ) + ln ^{2} ( 21 ) + 8 ln ( 7 ) ln ( 21 )}{2 ln ( 7 )}, x = \frac{ln ( 21 ) - ln ^{2} ( 21 ) + 8 ln ( 7 ) ln ( 21 )}{2 ln ( 7 )}

Dezimale

x = 2.71648 \dots, x = - 1.15191 \dots

Schritte zur Lösung

7^{x^{2} - x - 2} = 3^{x + 2}

Wende Exponentenregel an

(x^{2} - x - 2) ln (7) = (x + 2) ln (3)

Löse

(x^{2} - x - 2) ln (7) = (x + 2) ln (3) : x = \frac{ln ( 21 ) + ln ^{2} ( 21 ) + 8 ln ( 7 ) ln ( 21 )}{2 ln ( 7 )}, x = \frac{ln ( 21 ) - ln ^{2} ( 21 ) + 8 ln ( 7 ) ln ( 21 )}{2 ln ( 7 )}

x = \frac{ln ( 21 ) + ln ^{2} ( 21 ) + 8 ln ( 7 ) ln ( 21 )}{2 ln ( 7 )}, x = \frac{ln ( 21 ) - ln ^{2} ( 21 ) + 8 ln ( 7 ) ln ( 21 )}{2 ln ( 7 )}

10 0^{x} = 1000

1 1^{5 x - 2} = 5

8 1^{8^{x}} = 3^{3 2^{7}}

4^{x} - 32 = 4 (2^{x})

\frac{e ^{x} x - e ^{x}}{x ^{2}} = 0