10^{4x-8}=6^{10x+3}

Lösung

1 0^{4 x - 8} = 6^{10 x + 3}

x = \frac{3 ln ( 6 ) + 8 ln ( 10 )}{2 ln ( \frac{25}{1944} )}

Dezimale

x = - 2.73288 \dots

Schritte zur Lösung

1 0^{4 x - 8} = 6^{10 x + 3}

Wende Exponentenregel an

(4 x - 8) ln (10) = (10 x + 3) ln (6)

Löse

(4 x - 8) ln (10) = (10 x + 3) ln (6) : x = \frac{3 ln ( 6 ) + 8 ln ( 10 )}{2 ln ( \frac{25}{1944} )}

x = \frac{3 ln ( 6 ) + 8 ln ( 10 )}{2 ln ( \frac{25}{1944} )}

3^{x + 2} = 18

1.1 2^{x} = 2

4^{3 x - 5} = \frac{1}{256}

3000 = 3 \cdot 1 0^{x}

so l v e f or x, e^{- I n x} = 0.2