5^{x-1}=2^x

Lösung

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

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

Dezimale

x = 1.75647 \dots

Schritte zur Lösung

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

Wende Exponentenregel an

(x - 1) ln (5) = x ln (2)

Löse

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

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

2^{x} = 2048

3^{x + 2} = 5^{x - 1}

x^{3} = 3^{x}

e^{l n (x)} = 4

5^{x + 3} \cdot 5^{2 x - 4} = 125