5^{2x-1}=2(3^x)

Lösung

5^{2 x - 1} = 2 (3^{x})

x = \frac{ln ( 10 )}{2 ln ( 5 ) - ln ( 3 )}

Dezimale

x = 1.08599 \dots

Schritte zur Lösung

5^{2 x - 1} = 2 (3^{x})

Wende Exponentenregel an

(2 x - 1) ln (5) = ln (2) + x ln (3)

Löse

(2 x - 1) ln (5) = ln (2) + x ln (3) : x = \frac{ln ( 10 )}{2 ln ( 5 ) - ln ( 3 )}

x = \frac{ln ( 10 )}{2 ln ( 5 ) - ln ( 3 )}

3^{2 x} + 9^{x} = 162

e^{3 x} = 8

2 \cdot 2^{x} = \frac{2 ^{3 x}}{32}

e^{x} + 12 e^{- x} = 7

1 0^{2 x^{2} - 10 x + 1} = e