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

Lösung

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

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

Dezimale

x = 1.86906 \dots

Schritte zur Lösung

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

Wende Exponentenregel an

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

Löse

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

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

\frac{x}{8 \cdot 2 ^{5 x - 3}} = 24

12 5^{2 x} = \frac{5 ^{x - 3}}{625}

4782969 = 3^{x}

lo g_{2} (4^{x}) = - 2

(\frac{1}{4})^{x - 1} = 1 6^{x + 2}