3*6^x=4.5(e^2)^x

Lösung

3 \cdot 6^{x} = 4.5 (e^{2})^{x}

x = \frac{ln ( 4.5 ) - ln ( 3 )}{ln ( 6 ) - 2}

Dezimale

x = - 1.94709 \dots

Schritte zur Lösung

3 \cdot 6^{x} = 4.5 (e^{2})^{x}

Wende Exponentenregel an

ln (3) + x ln (6) = ln (4.5) + 2 x

Löse

ln (3) + x ln (6) = ln (4.5) + 2 x : x = \frac{ln ( 4.5 ) - ln ( 3 )}{ln ( 6 ) - 2}

x = \frac{ln ( 4.5 ) - ln ( 3 )}{ln ( 6 ) - 2}

so l v e f or x, 3^{x} = 27

so l v e f or x, 3^{x} = 81

3^{x} = 7^{1 - x}

so l v e f or x, 3^{x} = 4 y

4^{2 x} + 4^{x} - 20 = 0