5(2^{3x-2})=9^x

Lösung

5 (2^{3 x - 2}) = 9^{x}

x = \frac{ln ( 5 ) - 2 ln ( 2 )}{2 ln ( 3 ) - 3 ln ( 2 )}

Dezimale

x = 1.89453 \dots

Schritte zur Lösung

5 (2^{3 x - 2}) = 9^{x}

Wende Exponentenregel an

ln (5) + (3 x - 2) ln (2) = x ln (9)

Löse

ln (5) + (3 x - 2) ln (2) = x ln (9) : x = \frac{ln ( 5 ) - 2 ln ( 2 )}{2 ln ( 3 ) - 3 ln ( 2 )}

x = \frac{ln ( 5 ) - 2 ln ( 2 )}{2 ln ( 3 ) - 3 ln ( 2 )}

1 6^{9 x - 6} = (2^{4})^{6 + 7 x}

so l v e f or x, e^{e^{x}} = 2

8 = e^{t}

2^{t} = 43

91 = 3 1^{x}