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-(1/6 log_{2}(1/6)+5/6 log_{2}(5/6))

解答

化简

- (\frac{1}{6} lo g_{2} (\frac{1}{6}) + \frac{5}{6} lo g_{2} (\frac{5}{6}))

解答

- \frac{1}{6} lo g_{2} (\frac{3125}{46656})

+1

十进制

0.65002 \dots

求解步骤

- (\frac{1}{6} lo g_{2} (\frac{1}{6}) + \frac{5}{6} lo g_{2} (\frac{5}{6}))

使用对数计算法则:

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

\frac{1}{6} lo g_{2} (\frac{1}{6}) = lo g_{2} ((\frac{1}{6})^{\frac{1}{6}})

= - (\frac{5}{6} lo g_{2} (\frac{5}{6}) + lo g_{2} ((\frac{1}{6})^{\frac{1}{6}}))

使用对数计算法则:

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

\frac{5}{6} lo g_{2} (\frac{5}{6}) = lo g_{2} ((\frac{5}{6})^{\frac{5}{6}})

= - (lo g_{2} ((\frac{1}{6})^{\frac{1}{6}}) + lo g_{2} ((\frac{5}{6})^{\frac{5}{6}}))

使用对数计算法则:

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

lo g_{2} ((\frac{1}{6})^{\frac{1}{6}}) + lo g_{2} ((\frac{5}{6})^{\frac{5}{6}}) = lo g_{2} ((\frac{1}{6})^{\frac{1}{6}} (\frac{5}{6})^{\frac{5}{6}})

= - lo g_{2} ((\frac{1}{6})^{\frac{1}{6}} (\frac{5}{6})^{\frac{5}{6}})

化简

lo g_{2} ((\frac{1}{6})^{\frac{1}{6}} (\frac{5}{6})^{\frac{5}{6}}) : \frac{1}{6} lo g_{2} ((\frac{5}{6})^{5} \frac{1}{6})

= - \frac{1}{6} lo g_{2} ((\frac{5}{6})^{5} \frac{1}{6})

(\frac{5}{6})^{5} = \frac{5 ^{5}}{6 ^{5}}

= - \frac{1}{6} lo g_{2} (\frac{1}{6} \cdot \frac{5 ^{5}}{6 ^{5}})

乘

\frac{1}{6} \cdot \frac{5 ^{5}}{6 ^{5}} : \frac{3125}{46656}

= - \frac{1}{6} lo g_{2} (\frac{3125}{46656})

流行的例子

展开 y[(2x^2+x)(5x)]

e x p an d y [(2 x^{2} + x) (5 x)]

展开 sin(x)+1/(2pi)(x/(2pi)-1)

e x p an d sin (x) + \frac{1}{2 π} (\frac{x}{2 π} - 1)

展开-sin((k+1/2)pi)

e x p an d - sin ((k + \frac{1}{2}) π)

展开 (x)(((96-16x))/(12))^2

e x p an d (x) (\frac{( 96 - 16 x )}{12})^{2}

展开-2(e^x+e^xx)

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