3^x2^{1-x}=10

Lösung

3^{x} 2^{1 - x} = 10

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

Dezimale

x = 3.96936 \dots

Schritte zur Lösung

3^{x} \cdot 2^{1 - x} = 10

Wende Exponentenregel an

(lo g_{2} (3) x + 1 - x) ln (2) = ln (10)

Löse

(lo g_{2} (3) x + 1 - x) ln (2) = ln (10) : x = \frac{ln ( 5 )}{ln ( 3 ) - ln ( 2 )}

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

0 = - e^{3 x} + 3

x^{x} (ln (x) + 1) = 0

4^{x^{2}} \cdot 4^{5 x - 3} = 64

27 m^{3 x} = 1

2^{c} = 65536