2^{4x+1}=3^x

Lösung

2^{4 x + 1} = 3^{x}

x = - \frac{ln ( 2 )}{4 ln ( 2 ) - ln ( 3 )}

Dezimale

x = - 0.41407 \dots

Schritte zur Lösung

2^{4 x + 1} = 3^{x}

Wende Exponentenregel an

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

Löse

(4 x + 1) ln (2) = x ln (3) : x = - \frac{ln ( 2 )}{4 ln ( 2 ) - ln ( 3 )}

x = - \frac{ln ( 2 )}{4 ln ( 2 ) - ln ( 3 )}

4 e^{- x} x^{3} - e^{- x} x^{4} = 0

ln (9 e^{2 x}) = 1

30 + 50 e^{- 0.2 x} = 40

3 \times 4 e^{2 - 2 x} + 1 = 4

e^{2 x} + 2 e^{2 x} x = 0