(a)(3^{x-2})/((3^{-3))}=3^4

Lösung

(a) \frac{3 ^{x - 2}}{( 3 ^{- 3} )} = 3^{4}

x = \frac{ln ( \frac{81}{a} )}{ln ( 3 )} - 1

Schritte zur Lösung

(a) \frac{3 ^{x - 2}}{( 3 ^{- 3} )} = 3^{4}

Wende Exponentenregel an

(x + 1) ln (3) = ln (\frac{81}{a})

Löse

(x + 1) ln (3) = ln (\frac{81}{a}) : x = \frac{ln ( \frac{81}{a} )}{ln ( 3 )} - 1

x = \frac{ln ( \frac{81}{a} )}{ln ( 3 )} - 1

9^{x + 2} = 240 + 9^{x}

(27)^{x} = 3^{x} + 6

1 0^{x} = 5

3^{x} + 3 + 3^{x} - 27 = 2241

1 0^{x} = 2