3^{x+4}=6^{2x-5}

Lösung

3^{x + 4} = 6^{2 x - 5}

x = \frac{5 ln ( 6 ) + 4 ln ( 3 )}{ln ( 12 )}

Dezimale

x = 5.37374 \dots

Schritte zur Lösung

3^{x + 4} = 6^{2 x - 5}

Wende Exponentenregel an

(x + 4) ln (3) = (2 x - 5) ln (6)

Löse

(x + 4) ln (3) = (2 x - 5) ln (6) : x = \frac{5 ln ( 6 ) + 4 ln ( 3 )}{ln ( 12 )}

x = \frac{5 ln ( 6 ) + 4 ln ( 3 )}{ln ( 12 )}

5 (2^{x}) = 4

so l v e f or x, 3^{8 x} = 4^{- x - 7}

6^{x + 1} - 6^{x} = 1080

3 \cdot 5^{x + 3} - 5^{x + 1} = 74

2^{x} = 2500