2(3^{4x-5})=7^{2x}

Lösung

2 (3^{4 x - 5}) = 7^{2 x}

x = \frac{- ln ( 2 ) + 5 ln ( 3 )}{2 ( - ln ( 7 ) + 2 ln ( 3 ) )}

Dezimale

x = 9.54961 \dots

Schritte zur Lösung

2 (3^{4 x - 5}) = 7^{2 x}

Wende Exponentenregel an

ln (2) + (4 x - 5) ln (3) = 2 x ln (7)

Löse

ln (2) + (4 x - 5) ln (3) = 2 x ln (7) : x = \frac{- ln ( 2 ) + 5 ln ( 3 )}{2 ( - ln ( 7 ) + 2 ln ( 3 ) )}

x = \frac{- ln ( 2 ) + 5 ln ( 3 )}{2 ( - ln ( 7 ) + 2 ln ( 3 ) )}

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

(\frac{1}{2})^{x} = \frac{1}{32}

2 7^{x} = 9^{x - 2}

3^{x} = 60

4^{x^{2} - 6 x} = 16384