6(4^x)=5(3^{2x-3})

Lösung

6 (4^{x}) = 5 (3^{2 x - 3})

x = - \frac{ln ( 162 ) - ln ( 5 )}{2 ( ln ( 2 ) - ln ( 3 ) )}

Dezimale

x = 4.28909 \dots

Schritte zur Lösung

6 (4^{x}) = 5 (3^{2 x - 3})

Wende Exponentenregel an

ln (6) + x ln (4) = ln (5) + (2 x - 3) ln (3)

Löse

ln (6) + x ln (4) = ln (5) + (2 x - 3) ln (3) : x = - \frac{ln ( 162 ) - ln ( 5 )}{2 ( ln ( 2 ) - ln ( 3 ) )}

x = - \frac{ln ( 162 ) - ln ( 5 )}{2 ( ln ( 2 ) - ln ( 3 ) )}

e^{2 x} = 1

2 e^{x} = 3 e^{- x} + 5

e^{7 - 4 x} = 6

3^{x} = 27

7 (4^{x}) = 4 (6^{2 x - 2})