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

Lösung

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

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

Dezimale

x = - 0.64095 \dots

Schritte zur Lösung

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

Wende Exponentenregel an

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

Löse

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

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

7^{x - 2} - 3^{2 x + 1} = 0

so l v e f or m, n = 2^{m - 1}

3^{x - 6} = 2

1 6^{2 x} = 25 6^{2 x + 5}

3^{2 x + 1} - 18 (3^{x}) - 81 = 0