What is simplify-(1/6*log_{2}(1/6)+5/6*log_{2}(5/6)) ?

The solution to simplify-(1/6*log_{2}(1/6)+5/6*log_{2}(5/6)) is -1/6 log_{2}(3125/46656)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

simplify

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

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

Decimal Notation

0.65002 \dots

Solution steps

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

Apply log rule:

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}}))

Apply log rule:

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}}))

Apply log rule:

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}})

Simplify

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}})

Multiply

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

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

\frac{( - cos ( y ) ( 2 x sin ( y ) - cos ( x ) ) ) - 1}{x}

\frac{( 7 x + 8 ) ( 6 x + 4 )}{( x ^{2} - 16 ) ^{2}}

\frac{3 x}{( x - 2 ) ( x - 1 )}

\frac{1.2538 ( 1 + 0.16 s ) ( 1 + 0.16 s )}{s}

\frac{- 2 s ^{2} - 3 s - 11}{( s - 1 ) ( s + 2 ) ( s - 3 )}

What is simplify-(1/6*log_{2}(1/6)+5/6*log_{2}(5/6)) ?
The solution to simplify-(1/6*log_{2}(1/6)+5/6*log_{2}(5/6)) is -1/6 log_{2}(3125/46656)