81^{2^{x+7}}=2^{8^{x-13}}

Lösung

8 1^{2^{x + 7}} = 2^{8^{x - 13}}

x = \frac{46 ln ( 2 ) + ln ( 4 ln ( 3 ) ) - ln ( ln ( 2 ) )}{2 ln ( 2 )}

Dezimale

x = 24.33222 \dots

Schritte zur Lösung

8 1^{2^{x + 7}} = 2^{8^{x - 13}}

Wende Exponentenregel an

(x + 7) ln (2) + ln (ln (81)) = 3 (x - 13) ln (2) + ln (ln (2))

Löse

(x + 7) ln (2) + ln (ln (81)) = 3 (x - 13) ln (2) + ln (ln (2)) : x = \frac{46 ln ( 2 ) + ln ( 4 ln ( 3 ) ) - ln ( ln ( 2 ) )}{2 ln ( 2 )}

x = \frac{46 ln ( 2 ) + ln ( 4 ln ( 3 ) ) - ln ( ln ( 2 ) )}{2 ln ( 2 )}

1 5^{x} = 20

x^{x} = x^{2 x - 1}

2200 (1.04)^{x} = 8000

5 - e^{x} = 0

9 e^{3 x} = 27