3^{x/5}=2^{4x-2}

Lösung

3^{\frac{x}{5}} = 2^{4 x - 2}

x = \frac{10 ln ( 2 )}{20 ln ( 2 ) - ln ( 3 )}

Dezimale

x = 0.54303 \dots

Schritte zur Lösung

3^{\frac{x}{5}} = 2^{4 x - 2}

Wende Exponentenregel an

\frac{x}{5} ln (3) = (4 x - 2) ln (2)

Löse

\frac{x}{5} ln (3) = (4 x - 2) ln (2) : x = \frac{10 ln ( 2 )}{20 ln ( 2 ) - ln ( 3 )}

x = \frac{10 ln ( 2 )}{20 ln ( 2 ) - ln ( 3 )}

2^{x + 1} - 2^{x} = 8

5^{x} + 5^{x + 2} = 650

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

2 e^{3 x} = 5 e^{8 x}

- 3 e^{- 3 t} = 1