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Beliebt Algebra >

vereinfachen-(1/6)log_{2}(1/6)-(5/6)log_{2}(5/6)

Lösung

vereinfachen

- (\frac{1}{6}) lo g_{2} (\frac{1}{6}) - (\frac{5}{6}) lo g_{2} (\frac{5}{6})

Lösung

- \frac{1}{6} lo g_{2} (\frac{3125}{46656})

+1

Dezimale

0.65002 \dots

Schritte zur Lösung

- (\frac{1}{6}) lo g_{2} (\frac{1}{6}) - (\frac{5}{6}) lo g_{2} (\frac{5}{6})

Wende die log Regel an:

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

(\frac{1}{6}) lo g_{2} (\frac{1}{6}) = lo g_{2} ((\frac{1}{6})^{(\frac{1}{6})})

= - lo g_{2} ((\frac{1}{6})^{(\frac{1}{6})}) - (\frac{5}{6}) lo g_{2} (\frac{5}{6})

Wende die log Regel an:

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

(\frac{5}{6}) lo g_{2} (\frac{5}{6}) = lo g_{2} ((\frac{5}{6})^{(\frac{5}{6})})

= - lo g_{2} ((\frac{1}{6})^{(\frac{1}{6})}) - lo g_{2} ((\frac{5}{6})^{(\frac{5}{6})})

Schreibe

- lo g_{2} ((\frac{1}{6})^{(\frac{1}{6})}) - lo g_{2} ((\frac{5}{6})^{(\frac{5}{6})})

um:

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

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

Wende die log Regel an:

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

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

= - lo g_{2} ((\frac{1}{6})^{\frac{1}{6}} (\frac{5}{6})^{\frac{5}{6}})

Vereinfache

lo g_{2} ((\frac{1}{6})^{\frac{1}{6}} (\frac{5}{6})^{\frac{5}{6}}) : \frac{1}{6} lo g_{2} ((\frac{5}{6})^{5} \frac{1}{6})

= - \frac{1}{6} lo g_{2} ((\frac{5}{6})^{5} \frac{1}{6})

(\frac{5}{6})^{5} = \frac{5 ^{5}}{6 ^{5}}

= - \frac{1}{6} lo g_{2} (\frac{1}{6} \cdot \frac{5 ^{5}}{6 ^{5}})

Multipliziere

\frac{1}{6} \cdot \frac{5 ^{5}}{6 ^{5}} : \frac{3125}{46656}

= - \frac{1}{6} lo g_{2} (\frac{3125}{46656})

Beliebte Beispiele

vereinfachen log_{4}(5)+log_{4}(6)

s im pl i f y lo g_{4} (5) + lo g_{4} (6)

vereinfachen 2log_{5}(z)+2log_{5}(x)+10log_{5}(y)

s im pl i f y 2 lo g_{5} (z) + 2 lo g_{5} (x) + 10 lo g_{5} (y)

vereinfachen ln((sqrt(a^2-x^2))/x)

s im pl i f y ln (\frac{a ^{2} - x ^{2}}{x})

vereinfachen log_{4}(\sqrt[3]{x})-log_{4}(y)

s im pl i f y lo g_{4} (3 x) - lo g_{4} (y)

erweitern log_{10}(x^2y^4)

e x p an d lo g_{10} (x^{2} y^{4})