vereinfachen-0.9log_{2}(0.9)-0.1log_{2}(0.1)

Lösung

vereinfachen

- 0.9 lo g_{2} (0.9) - 0.1 lo g_{2} (0.1)

- lo g_{2} (0.72246 \dots)

Dezimale

0.46899 \dots

Schritte zur Lösung

- 0.9 lo g_{2} (0.9) - 0.1 lo g_{2} (0.1)

Wende die log Regel an:

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

0.9 lo g_{2} (0.9) = lo g_{2} (0. 9^{0.9})

= - lo g_{2} (0. 9^{0.9}) - 0.1 lo g_{2} (0.1)

Wende die log Regel an:

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

0.1 lo g_{2} (0.1) = lo g_{2} (0. 1^{0.1})

= - lo g_{2} (0. 9^{0.9}) - lo g_{2} (0. 1^{0.1})

Schreibe

- lo g_{2} (0. 9^{0.9}) - lo g_{2} (0. 1^{0.1})

um:

- (lo g_{2} (0. 9^{0.9}) + lo g_{2} (0. 1^{0.1}))

= - (lo g_{2} (0. 9^{0.9}) + lo g_{2} (0. 1^{0.1}))

Wende die log Regel an:

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

lo g_{2} (0. 9^{0.9}) + lo g_{2} (0. 1^{0.1}) = lo g_{2} (0. 9^{0.9} \cdot 0. 1^{0.1})

= - lo g_{2} (0. 9^{0.9} \cdot 0. 1^{0.1})

0. 9^{0.9} \cdot 0. 1^{0.1} = 0.72246 \dots

= - lo g_{2} (0.72246 \dots)

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