2^{x+2}=927^{x/((x-1))}

Lösung

2^{x + 2} = 92 7^{\frac{x}{( x - 1 )}}

x = \frac{- ln ( 2 ) + ln ( 927 ) + ( 9 ln ^{2} ( 2 ) - 2 ln ( 2 ) ln ( 927 ) + ln ^{2} ( 927 ) ) ^{\frac{1}{2}}}{2 ln ( 2 )}, x = \frac{- ln ( 2 ) + ln ( 927 ) - ( 9 ln ^{2} ( 2 ) - 2 ln ( 2 ) ln ( 927 ) + ln ^{2} ( 927 ) ) ^{\frac{1}{2}}}{2 ln ( 2 )}

Dezimale

x = 9.07676 \dots, x = - 0.22034 \dots

Schritte zur Lösung

2^{x + 2} = 92 7^{\frac{x}{( x - 1 )}}

Wende Exponentenregel an

(x + 2) ln (2) = \frac{x}{x - 1} ln (927)

Löse

(x + 2) ln (2) = \frac{x}{x - 1} ln (927) : x = \frac{- ln ( 2 ) + ln ( 927 ) + ( 9 ln ^{2} ( 2 ) - 2 ln ( 2 ) ln ( 927 ) + ln ^{2} ( 927 ) ) ^{\frac{1}{2}}}{2 ln ( 2 )}, x = \frac{- ln ( 2 ) + ln ( 927 ) - ( 9 ln ^{2} ( 2 ) - 2 ln ( 2 ) ln ( 927 ) + ln ^{2} ( 927 ) ) ^{\frac{1}{2}}}{2 ln ( 2 )}

x = \frac{- ln ( 2 ) + ln ( 927 ) + ( 9 ln ^{2} ( 2 ) - 2 ln ( 2 ) ln ( 927 ) + ln ^{2} ( 927 ) ) ^{\frac{1}{2}}}{2 ln ( 2 )}, x = \frac{- ln ( 2 ) + ln ( 927 ) - ( 9 ln ^{2} ( 2 ) - 2 ln ( 2 ) ln ( 927 ) + ln ^{2} ( 927 ) ) ^{\frac{1}{2}}}{2 ln ( 2 )}

9 = e^{x}

1 7^{2 x} = - 3^{- x - 10}

e^{x} + x = 0

4^{n} = 2

5. 3^{x} = 2