(14^{3x+1})(8^{2x+3})=7

Lösung

(1 4^{3 x + 1}) (8^{2 x + 3}) = 7

x = \frac{ln ( 7 ) - 9 ln ( 2 ) - 3 ln ( 2 ) lo g _{8} ( 14 )}{3 ln ( 2 ) ( 3 lo g _{8} ( 14 ) + 2 )}

Dezimale

x = - 0.57398 \dots

Schritte zur Lösung

(1 4^{3 x + 1}) (8^{2 x + 3}) = 7

Wende Exponentenregel an

(lo g_{8} (14) (3 x + 1) + 2 x + 3) ln (8) = ln (7)

Löse

(lo g_{8} (14) (3 x + 1) + 2 x + 3) ln (8) = ln (7) : x = \frac{ln ( 7 ) - 9 ln ( 2 ) - 3 ln ( 2 ) lo g _{8} ( 14 )}{3 ln ( 2 ) ( 3 lo g _{8} ( 14 ) + 2 )}

x = \frac{ln ( 7 ) - 9 ln ( 2 ) - 3 ln ( 2 ) lo g _{8} ( 14 )}{3 ln ( 2 ) ( 3 lo g _{8} ( 14 ) + 2 )}

5^{x} = 22

5^{x} = 23

5^{x} = 14

5^{x} = - 1

3^{2 x + 5} = 3^{7}