vereinfachen log_{sqrt(3)}(1/27)

Lösung

vereinfachen

lo g_{3} (\frac{1}{27})

- 6

Schritte zur Lösung

lo g_{3} (\frac{1}{27})

Wende Radikal Regel an:

a = a^{\frac{1}{2}}

3 = 3^{\frac{1}{2}}

= lo g_{3^{\frac{1}{2}}} (\frac{1}{27})

Wende die log Regel an:

lo g_{a^{b}} (x) = \frac{1}{b} lo g_{a} (x), a > 0

lo g_{3^{\frac{1}{2}}} (\frac{1}{27}) = \frac{1}{\frac{1}{2}} lo g_{3} (\frac{1}{27})

= \frac{1}{\frac{1}{2}} lo g_{3} (\frac{1}{27})

\frac{1}{27} = 3^{- 3}

= \frac{1}{\frac{1}{2}} lo g_{3} (3^{- 3})

Wende die log Regel an:

lo g_{a} (a^{b}) = b

lo g_{3} (3^{- 3}) = - 3

= \frac{1}{\frac{1}{2}} (- 3)

\frac{1}{\frac{1}{2}} (- 3) = - 6

= - 6

f a c t or b^{2} - 16

f a c t or x^{3} - 7 x

f a c t or 2 x^{2} + 8 x - 24

3 x^{2} - 21 x = 24

f a c t or x^{3} - 5 x^{2} + 6 x