What is (3/11)log_{2}(3/11)+(8/11)log_{2}(8/11) ?

The solution to (3/11)log_{2}(3/11)+(8/11)log_{2}(8/11) is (log_{2}(27/285311670611)+24)/(11)

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simplify (3/11)log_{2}(3/11)+(8/11)log_{2}(8/11)

simplify

(\frac{3}{11}) lo g_{2} (\frac{3}{11}) + (\frac{8}{11}) lo g_{2} (\frac{8}{11})

\frac{lo g _{2} ( \frac{27}{285311670611} ) + 24}{11}

Decimal Notation

- 0.84535 \dots

Solution steps

(\frac{3}{11}) lo g_{2} (\frac{3}{11}) + (\frac{8}{11}) lo g_{2} (\frac{8}{11})

(\frac{3}{11}) lo g_{2} (\frac{3}{11}) = \frac{3}{11} lo g_{2} (\frac{3}{11})

(\frac{8}{11}) lo g_{2} (\frac{8}{11}) = \frac{8}{11} lo g_{2} (\frac{8}{11})

= \frac{3}{11} lo g_{2} (\frac{3}{11}) + \frac{8}{11} lo g_{2} (\frac{8}{11})

\frac{3}{11} lo g_{2} (\frac{3}{11}) = lo g_{2} ((\frac{3}{11})^{\frac{3}{11}})

\frac{8}{11} lo g_{2} (\frac{8}{11}) = lo g_{2} ((\frac{8}{11})^{\frac{8}{11}})

= lo g_{2} ((\frac{3}{11})^{\frac{3}{11}}) + lo g_{2} ((\frac{8}{11})^{\frac{8}{11}})

Apply log rule:

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

lo g_{2} ((\frac{3}{11})^{\frac{3}{11}}) + lo g_{2} ((\frac{8}{11})^{\frac{8}{11}}) = lo g_{2} ((\frac{3}{11})^{\frac{3}{11}} (\frac{8}{11})^{\frac{8}{11}})

= lo g_{2} ((\frac{3}{11})^{\frac{3}{11}} (\frac{8}{11})^{\frac{8}{11}})

Apply log rule:

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

= \frac{lo g _{2} ( \frac{27}{285311670611} ) + 24}{11}

\frac{1}{1828} ln (\frac{1814}{1828 - 1814})

ln (\frac{87.4}{151.5})

lo g_{8} (3) + 4 lo g_{8} (r)

lo g_{3} (\frac{5 x ^{4}}{y ^{3}})

ln (i) - ln (i - n)

What is (3/11)log_{2}(3/11)+(8/11)log_{2}(8/11) ?
The solution to (3/11)log_{2}(3/11)+(8/11)log_{2}(8/11) is (log_{2}(27/285311670611)+24)/(11)