2^{x-5}=5^{2x+6}

Lösung

2^{x - 5} = 5^{2 x + 6}

x = \frac{6 ln ( 5 ) + 5 ln ( 2 )}{ln ( 2 ) - 2 ln ( 5 )}

Dezimale

x = - 5.19547 \dots

Schritte zur Lösung

2^{x - 5} = 5^{2 x + 6}

Wende Exponentenregel an

(x - 5) ln (2) = (2 x + 6) ln (5)

Löse

(x - 5) ln (2) = (2 x + 6) ln (5) : x = \frac{6 ln ( 5 ) + 5 ln ( 2 )}{ln ( 2 ) - 2 ln ( 5 )}

x = \frac{6 ln ( 5 ) + 5 ln ( 2 )}{ln ( 2 ) - 2 ln ( 5 )}

3^{x + 2} + 3^{x + 1} = 108

e^{x} - 3 e^{- x} - 2 = 0

8^{2 x + 1} = 12 8^{x - 3}

1.0 3^{x} = 2

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