erweitern log_{10}(sqrt(x^2(x+2)))

Lösung

erweitern

lo g_{10} (x^{2} (x + 2))

lo g_{10} (x) + \frac{1}{2} lo g_{10} (x + 2)

Schritte zur Lösung

lo g_{10} (x^{2} (x + 2))

x^{2} (x + 2) = x x + 2

= lo g_{10} (x x + 2)

Wende die log Regel an:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{10} (x x + 2) = lo g_{10} (x) + lo g_{10} (x + 2)

= lo g_{10} (x) + lo g_{10} (x + 2)

Vereinfache

lo g_{10} (x + 2) : \frac{1}{2} lo g_{10} (x + 2)

= lo g_{10} (x) + \frac{1}{2} lo g_{10} (x + 2)

e x p an d \frac{4 x ^{2} + 6 x + 11}{( x + 2 ) ( x ^{2} + x + 3 )}

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s im pl i f y (7 x^{\frac{5}{3}} + 49 x^{\frac{2}{3}}) (5)