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

Lösung

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

x = \frac{ln ( 4375 ) - ln ( 3 )}{5 ln ( 5 ) - ln ( 3 )}

Dezimale

x = 1.04842 \dots

Schritte zur Lösung

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

Wende Exponentenregel an

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

Löse

ln (7) + x ln (3) = ln (3) + (5 x - 4) ln (5) : x = \frac{ln ( 4375 ) - ln ( 3 )}{5 ln ( 5 ) - ln ( 3 )}

x = \frac{ln ( 4375 ) - ln ( 3 )}{5 ln ( 5 ) - ln ( 3 )}

4^{x + 1} = \frac{1}{8 2}

5^{3 x + 4} = 45

2 \cdot 5^{x + 1} = 250

4^{9 x + 4} = 3

3^{2 x - 1} = 4 \cdot 3^{x - 1} - 1