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

Lösung

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

x = \frac{ln ( 6 )}{ln ( 75 ) - ln ( 2 )}

Dezimale

x = 0.49436 \dots

Schritte zur Lösung

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

Wende Exponentenregel an

(lo g_{2} (3) x + lo g_{2} (5) \cdot 2 x) ln (2) = ln (6) + x ln (2)

Löse

(lo g_{2} (3) x + lo g_{2} (5) \cdot 2 x) ln (2) = ln (6) + x ln (2) : x = \frac{ln ( 6 )}{ln ( 75 ) - ln ( 2 )}

x = \frac{ln ( 6 )}{ln ( 75 ) - ln ( 2 )}

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

\frac{2 7 ^{2}}{8 1 ^{3}} = 3^{x}

2 e^{x} - 9 e^{- 3 x} = 0

(\frac{4}{3})^{1 - x} = 5^{x}

95 = 1 1^{x}