2^{5k+3}=3^{550}

Lösung

2^{5 k + 3} = 3^{550}

k = \frac{550 ln ( 3 ) - 3 ln ( 2 )}{5 ln ( 2 )}

Dezimale

k = 173.74587 \dots

Schritte zur Lösung

2^{5 k + 3} = 3^{550}

Wende Exponentenregel an

(5 k + 3) ln (2) = 550 ln (3)

Löse

(5 k + 3) ln (2) = 550 ln (3) : k = \frac{550 ln ( 3 ) - 3 ln ( 2 )}{5 ln ( 2 )}

k = \frac{550 ln ( 3 ) - 3 ln ( 2 )}{5 ln ( 2 )}

so l v e f or b, a^{b} = 144 a - 1

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

\frac{3 ^{\frac{x}{2}} + 3}{3 ^{\frac{x}{2}}} = 4

2^{t} = 0

1 0^{c} = 10000