2^{x+2}+2^{x-1}=6^{x-1}

Lösung

2^{x + 2} + 2^{x - 1} = 6^{x - 1}

x = 3

Schritte zur Lösung

2^{x + 2} + 2^{x - 1} = 6^{x - 1}

Vereinfache

2^{x + 2} + 2^{x - 1} : 9 \cdot 2^{x - 1}

9 \cdot 2^{x - 1} = 6^{x - 1}

Wende Exponentenregel an

ln (9) + (x - 1) ln (2) = (x - 1) ln (6)

Löse

ln (9) + (x - 1) ln (2) = (x - 1) ln (6) : x = 3

x = 3

288 \cdot 2^{\frac{x}{4}} = 96

25 = \frac{100 ( 0.5 ) ^{t}}{5730}

2 (7^{x}) = 686

9^{- x} = 27

49 e^{7 x} + e^{- x} = 0