3^{x^2}=7^{6-x}

Lösung

3^{x^{2}} = 7^{6 - x}

x = \frac{- ln ( 7 ) + ln ^{2} ( 7 ) + 24 ln ( 3 ) ln ( 7 )}{2 ln ( 3 )}, x = \frac{- ln ( 7 ) - ln ^{2} ( 7 ) + 24 ln ( 3 ) ln ( 7 )}{2 ln ( 3 )}

Dezimale

x = 2.49251 \dots, x = - 4.26375 \dots

Schritte zur Lösung

3^{x^{2}} = 7^{6 - x}

Wende Exponentenregel an

x^{2} ln (3) = (6 - x) ln (7)

Löse

x^{2} ln (3) = (6 - x) ln (7) : x = \frac{- ln ( 7 ) + ln ^{2} ( 7 ) + 24 ln ( 3 ) ln ( 7 )}{2 ln ( 3 )}, x = \frac{- ln ( 7 ) - ln ^{2} ( 7 ) + 24 ln ( 3 ) ln ( 7 )}{2 ln ( 3 )}

x = \frac{- ln ( 7 ) + ln ^{2} ( 7 ) + 24 ln ( 3 ) ln ( 7 )}{2 ln ( 3 )}, x = \frac{- ln ( 7 ) - ln ^{2} ( 7 ) + 24 ln ( 3 ) ln ( 7 )}{2 ln ( 3 )}

2 e^{2 x} = e^{x} + 10

2^{x x} = 2^{27}

4^{2 x + 1} = 3 2^{3 x}

7^{2 x + 1} - 2 \times 7^{x + 1} + 7 = 0

3^{1 - y} - 3^{y} = 2