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

Lösung

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

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

Dezimale

x = 0.86606 \dots

Schritte zur Lösung

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

Wende Exponentenregel an

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

Löse

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

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

2^{x - 1} = 1

81 = 3^{x}

3^{2 x} = 27

2^{x} = x^{100}

lo g_{2} (16) = 8 \cdot 2^{- x}