zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的代数 >

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

解答

化简

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

解答

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

+1

十进制

0.94028 \dots

求解步骤

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

使用对数计算法则:

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}}))

使用对数计算法则:

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}}))

使用对数计算法则:

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}})

化简

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}})

乘

\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}})

流行的例子

展开 2e^{x^2-4x}(2x-4)

e x p an d 2 e^{x^{2} - 4 x} (2 x - 4)

展开-(3x+8-(-15+6x-(-3x+2)-(5x+4)-29)=-5)

e x p an d - (3 x + 8 - (- 15 + 6 x - (- 3 x + 2) - (5 x + 4) - 29) = - 5)

展开 cos(2(t-2pi))

e x p an d cos (2 (t - 2 π))

e x p an d 3 c - 3

展开 (2(x+2))/5

e x p an d \frac{2 ( x + 2 )}{5}