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人気のある代数 >

簡約-0.43log_{2}(0.43)-0.57log_{2}(0.57)

解

簡約

- 0.43 lo g_{2} (0.43) - 0.57 lo g_{2} (0.57)

解

- lo g_{2} (\frac{5 7 ^{0.57} \cdot 4 3 ^{0.43}}{25}) + 2

+1

十進法表記

0.98581 \dots

解答ステップ

- 0.43 lo g_{2} (0.43) - 0.57 lo g_{2} (0.57)

- 0.43 lo g_{2} (0.43) = - 0.43 lo g_{2} (\frac{43}{100})

0.57 = \frac{57}{100}

= - 0.43 lo g_{2} (\frac{43}{100}) - 0.57 lo g_{2} (\frac{57}{100})

- 0.43 lo g_{2} (\frac{43}{100}) = - lo g_{2} ((\frac{43}{100})^{0.43})

- 0.57 lo g_{2} (\frac{57}{100}) = - lo g_{2} ((\frac{57}{100})^{0.57})

= - lo g_{2} ((\frac{43}{100})^{0.43}) - lo g_{2} ((\frac{57}{100})^{0.57})

対数の規則を適用する:

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

- lo g_{2} ((\frac{57}{100})^{0.57}) - lo g_{2} ((\frac{43}{100})^{0.43}) = lo g_{2} ((\frac{57}{100})^{0.57} (\frac{43}{100})^{0.43})

= - lo g_{2} ((\frac{57}{100})^{0.57} (\frac{43}{100})^{0.43})

簡素化

(\frac{57}{100})^{0.57} (\frac{43}{100})^{0.43} : \frac{5 7 ^{0.57} \cdot 4 3 ^{0.43}}{100}

= - lo g_{2} (\frac{5 7 ^{0.57} \cdot 4 3 ^{0.43}}{100})

対数の規則を適用する:

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

lo g_{2} (\frac{5 7 ^{0.57} \cdot 4 3 ^{0.43}}{100}) = lo g_{2} (5 7^{0.57} \cdot 4 3^{0.43}) - lo g_{2} (100)

= - (lo g_{2} (5 7^{0.57} \cdot 4 3^{0.43}) - lo g_{2} (100))

lo g_{2} (5 7^{0.57} \cdot 4 3^{0.43}) = 0.57 lo g_{2} (57) + 0.43 lo g_{2} (43)

= - ((0.57 lo g_{2} (57) + 0.43 lo g_{2} (43)) - lo g_{2} (100))

規則を適用する:

(a) = a

(0.57 lo g_{2} (57) + 0.43 lo g_{2} (43)) = 0.57 lo g_{2} (57) + 0.43 lo g_{2} (43)

= - (0.57 lo g_{2} (57) + 0.43 lo g_{2} (43) - lo g_{2} (100))

lo g_{2} (100) = 2 + 2 lo g_{2} (5)

= - (0.57 lo g_{2} (57) + 0.43 lo g_{2} (43) - (2 + 2 lo g_{2} (5)))

分配法則を適用する:

- (a + b) = - a - b

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

= - (0.57 lo g_{2} (57) + 0.43 lo g_{2} (43) - 2 - 2 lo g_{2} (5))

0.57 lo g_{2} (57) = lo g_{2} (5 7^{0.57})

0.43 lo g_{2} (43) = lo g_{2} (4 3^{0.43})

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

= - (lo g_{2} (5 7^{0.57}) + lo g_{2} (4 3^{0.43}) - 2 - lo g_{2} (5^{2}))

lo g_{2} (5 7^{0.57}) + lo g_{2} (4 3^{0.43}) - lo g_{2} (5^{2}) = lo g_{2} (\frac{5 7 ^{0.57} \cdot 4 3 ^{0.43}}{25})

= - (lo g_{2} (\frac{5 7 ^{0.57} \cdot 4 3 ^{0.43}}{25}) - 2)

分配法則を適用する:

- (a - b) = - a + b

- (lo g_{2} (\frac{5 7 ^{0.57} \cdot 4 3 ^{0.43}}{25}) - 2) = - lo g_{2} (\frac{5 7 ^{0.57} \cdot 4 3 ^{0.43}}{25}) + 2

= - lo g_{2} (\frac{5 7 ^{0.57} \cdot 4 3 ^{0.43}}{25}) + 2

人気の例

展開する log_{b}(x^4y)

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

簡約 4log_{b}(y)+6log_{b}(w)

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

展開する ln((e^4)/3)

e x p an d ln (\frac{e ^{4}}{3})

簡約 ln((0.003789035)/(0.001129995))

s im pl i f y ln (\frac{0.003789035}{0.001129995})

簡約 ln(6/16)

s im pl i f y ln (\frac{6}{16})