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simplificar-0.55log_{2}(0.55)-0.45log_{2}(0.45)

Solución

simplificar

- 0.55 lo g_{2} (0.55) - 0.45 lo g_{2} (0.45)

- lo g_{2} (\frac{3 ^{0.9} \cdot 1 1 ^{0.55}}{5}) + 2

Notación decimal

0.99277 \dots

Pasos de solución

- 0.55 lo g_{2} (0.55) - 0.45 lo g_{2} (0.45)

- 0.55 lo g_{2} (0.55) = - 0.55 lo g_{2} (\frac{11}{20})

lo g_{2} (0.45) = lo g_{2} (\frac{9}{20})

= - 0.55 lo g_{2} (\frac{11}{20}) - 0.45 lo g_{2} (\frac{9}{20})

- 0.55 lo g_{2} (\frac{11}{20}) = - lo g_{2} ((\frac{11}{20})^{0.55})

- 0.45 lo g_{2} (\frac{9}{20}) = - lo g_{2} ((\frac{9}{20})^{0.45})

= - lo g_{2} ((\frac{11}{20})^{0.55}) - lo g_{2} ((\frac{9}{20})^{0.45})

Aplicar las propiedades de los logaritmos:

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

- lo g_{2} ((\frac{9}{20})^{0.45}) - lo g_{2} ((\frac{11}{20})^{0.55}) = lo g_{2} ((\frac{9}{20})^{0.45} (\frac{11}{20})^{0.55})

= - lo g_{2} ((\frac{9}{20})^{0.45} (\frac{11}{20})^{0.55})

Simplificar

(\frac{9}{20})^{0.45} (\frac{11}{20})^{0.55} : \frac{9 ^{0.45} \cdot 1 1 ^{0.55}}{20}

= - lo g_{2} (\frac{9 ^{0.45} \cdot 1 1 ^{0.55}}{20})

Aplicar las propiedades de los logaritmos:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{2} (\frac{9 ^{0.45} \cdot 1 1 ^{0.55}}{20}) = lo g_{2} (9^{0.45} \cdot 1 1^{0.55}) - lo g_{2} (20)

= - (lo g_{2} (9^{0.45} \cdot 1 1^{0.55}) - lo g_{2} (20))

lo g_{2} (20) = 2 + lo g_{2} (5)

= - (lo g_{2} (9^{0.45} \cdot 1 1^{0.55}) - (2 + lo g_{2} (5)))

Poner los parentesis utilizando:

- (a + b) = - a - b

- (2 + lo g_{2} (5)) = - 2 - lo g_{2} (5)

= - (lo g_{2} (9^{0.45} \cdot 1 1^{0.55}) - 2 - lo g_{2} (5))

lo g_{2} (9^{0.45} \cdot 1 1^{0.55}) = 0.9 lo g_{2} (3) + 0.55 lo g_{2} (11)

= - ((0.9 lo g_{2} (3) + 0.55 lo g_{2} (11)) - 2 - lo g_{2} (5))

Aplicar la propiedad:

(a) = a

(0.9 lo g_{2} (3) + 0.55 lo g_{2} (11)) = 0.9 lo g_{2} (3) + 0.55 lo g_{2} (11)

= - (0.9 lo g_{2} (3) + 0.55 lo g_{2} (11) - 2 - lo g_{2} (5))

0.9 lo g_{2} (3) = lo g_{2} (3^{0.9})

0.55 lo g_{2} (11) = lo g_{2} (1 1^{0.55})

= - (lo g_{2} (3^{0.9}) + lo g_{2} (1 1^{0.55}) - 2 - lo g_{2} (5))

lo g_{2} (3^{0.9}) + lo g_{2} (1 1^{0.55}) - lo g_{2} (5) = lo g_{2} (\frac{3 ^{0.9} \cdot 1 1 ^{0.55}}{5})

= - (lo g_{2} (\frac{3 ^{0.9} \cdot 1 1 ^{0.55}}{5}) - 2)

Poner los parentesis utilizando:

- (a - b) = - a + b

- (lo g_{2} (\frac{3 ^{0.9} \cdot 1 1 ^{0.55}}{5}) - 2) = - lo g_{2} (\frac{3 ^{0.9} \cdot 1 1 ^{0.55}}{5}) + 2

= - lo g_{2} (\frac{3 ^{0.9} \cdot 1 1 ^{0.55}}{5}) + 2

lo g_{2} (\frac{x}{y})

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