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Beliebt Algebra >

vereinfachen-(9/14 log_{2}(9/14)+5/14 log_{2}(5/14))

Lösung

vereinfachen

- (\frac{9}{14} lo g_{2} (\frac{9}{14}) + \frac{5}{14} lo g_{2} (\frac{5}{14}))

Lösung

- \frac{1}{14} lo g_{2} (\frac{1210689028125}{1 4 ^{14}})

+1

Dezimale

0.94028 \dots

Schritte zur Lösung

- (\frac{9}{14} lo g_{2} (\frac{9}{14}) + \frac{5}{14} lo g_{2} (\frac{5}{14}))

Wende die log Regel an:

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

\frac{9}{14} lo g_{2} (\frac{9}{14}) = lo g_{2} ((\frac{9}{14})^{\frac{9}{14}})

= - (\frac{5}{14} lo g_{2} (\frac{5}{14}) + lo g_{2} ((\frac{9}{14})^{\frac{9}{14}}))

Wende die log Regel an:

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

\frac{5}{14} lo g_{2} (\frac{5}{14}) = lo g_{2} ((\frac{5}{14})^{\frac{5}{14}})

= - (lo g_{2} ((\frac{9}{14})^{\frac{9}{14}}) + lo g_{2} ((\frac{5}{14})^{\frac{5}{14}}))

Wende die log Regel an:

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

lo g_{2} ((\frac{9}{14})^{\frac{9}{14}}) + lo g_{2} ((\frac{5}{14})^{\frac{5}{14}}) = lo g_{2} ((\frac{9}{14})^{\frac{9}{14}} (\frac{5}{14})^{\frac{5}{14}})

= - lo g_{2} ((\frac{9}{14})^{\frac{9}{14}} (\frac{5}{14})^{\frac{5}{14}})

Vereinfache

lo g_{2} ((\frac{9}{14})^{\frac{9}{14}} (\frac{5}{14})^{\frac{5}{14}}) : \frac{1}{14} lo g_{2} ((\frac{9}{14})^{9} (\frac{5}{14})^{5})

= - \frac{1}{14} lo g_{2} ((\frac{9}{14})^{9} (\frac{5}{14})^{5})

(\frac{9}{14})^{9} = \frac{9 ^{9}}{1 4 ^{9}}

= - \frac{1}{14} lo g_{2} ((\frac{5}{14})^{5} \frac{9 ^{9}}{1 4 ^{9}})

(\frac{5}{14})^{5} = \frac{5 ^{5}}{1 4 ^{5}}

= - \frac{1}{14} lo g_{2} (\frac{9 ^{9}}{1 4 ^{9}} \cdot \frac{5 ^{5}}{1 4 ^{5}})

Multipliziere

\frac{9 ^{9}}{1 4 ^{9}} \cdot \frac{5 ^{5}}{1 4 ^{5}} : \frac{1210689028125}{1 4 ^{14}}

= - \frac{1}{14} lo g_{2} (\frac{1210689028125}{1 4 ^{14}})

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