vereinfachen-(3/11)log_{2}(3/11)-(8/11)log_{2}(8/11)

Lösung

vereinfachen

- (\frac{3}{11}) lo g_{2} (\frac{3}{11}) - (\frac{8}{11}) lo g_{2} (\frac{8}{11})

- \frac{lo g _{2} ( \frac{27}{285311670611} ) + 24}{11}

Dezimale

0.84535 \dots

Schritte zur Lösung

- (\frac{3}{11}) lo g_{2} (\frac{3}{11}) - (\frac{8}{11}) lo g_{2} (\frac{8}{11})

Apply rule:

(a) = a

(\frac{3}{11}) = \frac{3}{11}

= - \frac{3}{11} lo g_{2} (\frac{3}{11}) - \frac{8}{11} lo g_{2} (\frac{8}{11})

- \frac{3}{11} lo g_{2} (\frac{3}{11}) = - lo g_{2} ((\frac{3}{11})^{\frac{3}{11}})

- \frac{8}{11} lo g_{2} (\frac{8}{11}) = - lo g_{2} ((\frac{8}{11})^{\frac{8}{11}})

= - lo g_{2} ((\frac{3}{11})^{\frac{3}{11}}) - lo g_{2} ((\frac{8}{11})^{\frac{8}{11}})

Wende die log Regel an:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

- lo g_{2} ((\frac{8}{11})^{\frac{8}{11}}) - lo g_{2} ((\frac{3}{11})^{\frac{3}{11}}) = lo g_{2} ((\frac{8}{11})^{\frac{8}{11}} (\frac{3}{11})^{\frac{3}{11}})

= - lo g_{2} ((\frac{8}{11})^{\frac{8}{11}} (\frac{3}{11})^{\frac{3}{11}})

(\frac{8}{11})^{\frac{8}{11}} (\frac{3}{11})^{\frac{3}{11}} = \frac{4 11 4}{11 214358881} 11 \frac{27}{1331}

= - lo g_{2} (\frac{4 11 4}{11 214358881} 11 \frac{27}{1331})

Wende die log Regel an:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{2} (\frac{4 11 4}{11 214358881} 11 \frac{27}{1331}) = lo g_{2} (\frac{4 11 4}{11 214358881}) + lo g_{2} (11 \frac{27}{1331})

= - (lo g_{2} (\frac{4 11 4}{11 214358881}) + lo g_{2} (11 \frac{27}{1331}))

lo g_{2} (\frac{4 11 4}{11 214358881}) = \frac{24 - 11 lo g _{2} ( 11 214358881 )}{11}

= - (\frac{24 - 11 lo g _{2} ( 11 214358881 )}{11} + lo g_{2} (11 \frac{27}{1331}))

\frac{24 - 11 lo g _{2} ( 11 214358881 )}{11} + lo g_{2} (11 \frac{27}{1331}) = \frac{lo g _{2} ( 11 \frac{27}{1331} ) \cdot 11 + 24 - 11 lo g _{2} ( 11 214358881 )}{11}

= - \frac{lo g _{2} ( 11 \frac{27}{1331} ) \cdot 11 + 24 - 11 lo g _{2} ( 11 214358881 )}{11}

= - \frac{11 lo g _{2} ( 11 \frac{27}{1331} ) + 24 - 11 lo g _{2} ( 11 214358881 )}{11}

11 lo g_{2} (11 \frac{27}{1331}) + 24 - 11 lo g_{2} (11214358881) = lo g_{2} (\frac{27}{285311670611}) + 24

= - \frac{lo g _{2} ( \frac{27}{285311670611} ) + 24}{11}

s im pl i f y ln (\frac{2 ^{4}}{3 ^{4} 5 ^{3}})

s im pl i f y ln (4 π)

s im pl i f y lo g_{3} (c) + lo g_{3} (c + 2)

s im pl i f y \frac{1}{3} lo g_{2} (x) + \frac{1}{2} lo g_{2} (y) + lo g_{2} (z)

s im pl i f y ln (2) + ln (9)