vereinfachen (log_{10}(a)log_{10}(c)blog_{10}(a))^3

Lösung

vereinfachen

(lo g_{10} (a) lo g_{10} (c) b lo g_{10} (a))^{3}

b^{3} lo g_{10} (a)^{6} lo g_{10} (c)^{3}

Schritte zur Lösung

(lo g_{10} (a) lo g_{10} (c) b lo g_{10} (a))^{3}

Wende Exponentenregel an:

(a \cdot b)^{n} = a^{n} b^{n}

(lo g_{10} (a) lo g_{10} (c) b lo g_{10} (a))^{3} = lo g_{10} (a)^{3} lo g_{10} (c)^{3} b^{3} lo g_{10} (a)^{3}

= lo g_{10} (a)^{3} lo g_{10} (c)^{3} b^{3} lo g_{10} (a)^{3}

Wende Exponentenregel an:

a^{m} b^{m} = (ab)^{m},

angenommen

a \geq 0, b \geq 0

b^{3} lo g_{10} (a)^{3} lo g_{10} (a)^{3} lo g_{10} (c)^{3} = (b lo g_{10} (a) lo g_{10} (a) lo g_{10} (c))^{3}

= (b lo g_{10} (a) lo g_{10} (a) lo g_{10} (c))^{3}

Vereinfache

lo g_{10} (a) lo g_{10} (c) b lo g_{10} (a) : b lo g_{10} (a)^{2} lo g_{10} (c)

= (b lo g_{10} (a)^{2} lo g_{10} (c))^{3}

Wende Exponentenregel an:

(a \cdot b)^{n} = a^{n} b^{n}

= b^{3} lo g_{10} (c)^{3} (lo g_{10} (a)^{2})^{3}

(lo g_{10} (a)^{2})^{3} : lo g_{10} (a)^{6}

= b^{3} lo g_{10} (a)^{6} lo g_{10} (c)^{3}

j o in 2 - (\frac{3 x}{7})

s im pl i f y \frac{1 - tan ^{2} ( x ) + 1}{cos ^{2} ( x )}

f a c t or 4 m^{4} + 35 m^{2} n^{2} + 121 n^{4}

e x p an d (4 x^{2} - 1) (4 x^{2} + 1)

s im pl i f y \frac{2 x ^{4} - 3 x ^{4} + 3 x ^{2}}{x ^{6}}