vereinfachen 2log_{5}(5x^3)+1/3 log_{5}(x^2+6)

Lösung

vereinfachen

2 lo g_{5} (5 x^{3}) + \frac{1}{3} lo g_{5} (x^{2} + 6)

lo g_{5} (25 x^{6} 3 x^{2} + 6)

Schritte zur Lösung

2 lo g_{5} (5 x^{3}) + \frac{1}{3} lo g_{5} (x^{2} + 6)

2 lo g_{5} (5 x^{3}) = lo g_{5} ((5 x^{3})^{2})

\frac{1}{3} lo g_{5} (x^{2} + 6) = lo g_{5} ((x^{2} + 6)^{\frac{1}{3}})

= lo g_{5} ((5 x^{3})^{2}) + lo g_{5} ((x^{2} + 6)^{\frac{1}{3}})

Wende die log Regel an:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{5} ((5 x^{3})^{2}) + lo g_{5} ((x^{2} + 6)^{\frac{1}{3}}) = lo g_{5} ((5 x^{3})^{2} (x^{2} + 6)^{\frac{1}{3}})

= lo g_{5} ((5 x^{3})^{2} (x^{2} + 6)^{\frac{1}{3}})

Vereinfache

(5 x^{3})^{2} : 25 x^{6}

= lo g_{5} (25 x^{6} (x^{2} + 6)^{\frac{1}{3}})

Wende Exponentenregel an:

a^{\frac{1}{n}} = n a

(x^{2} + 6)^{\frac{1}{3}} = 3 x^{2} + 6

= lo g_{5} (25 x^{6} 3 x^{2} + 6)

\frac{7}{5} = \frac{x}{7}

(x + 1) (x + 1) = 1

5 x^{2} + 470 = - 100 x

3 ∣ 2 x - 7 ∣ = 3

\frac{3 X + 2}{X - 1} > 0