5^{x+1}=2(3^{2x})

Lösung

5^{x + 1} = 2 (3^{2 x})

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

Dezimale

x = 1.55888 \dots

Schritte zur Lösung

5^{x + 1} = 2 (3^{2 x})

Wende Exponentenregel an

(x + 1) ln (5) = ln (2) + 2 x ln (3)

Löse

(x + 1) ln (5) = ln (2) + 2 x ln (3) : x = \frac{ln ( 5 ) - ln ( 2 )}{2 ln ( 3 ) - ln ( 5 )}

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

4^{2 p} = 4^{- 2 p - 1}

2^{3 x + 1} = 4

so l v e f or x, e^{2 x} - e^{x} = 0

3^{5 + 4 x} = 9^{x}

so l v e f or y, x = 6^{3 + 2 y}