What is simplify-8/14 log_{2}(8/14)-6/14 log_{2}(6/14) ?

The solution to simplify-8/14 log_{2}(8/14)-6/14 log_{2}(6/14) is -(log_{2}((27)/(7^7))+8)/7

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simplify-8/14 log_{2}(8/14)-6/14 log_{2}(6/14)

simplify

- \frac{8}{14} lo g_{2} (\frac{8}{14}) - \frac{6}{14} lo g_{2} (\frac{6}{14})

- \frac{lo g _{2} ( \frac{27}{7 ^{7}} ) + 8}{7}

Decimal Notation

0.98522 \dots

Solution steps

- \frac{8}{14} lo g_{2} (\frac{8}{14}) - \frac{6}{14} lo g_{2} (\frac{6}{14})

- \frac{8}{14} lo g_{2} (\frac{8}{14}) = - \frac{4}{7} lo g_{2} (\frac{4}{7})

\frac{6}{14} lo g_{2} (\frac{6}{14}) = \frac{3}{7} lo g_{2} (\frac{3}{7})

= - \frac{4}{7} lo g_{2} (\frac{4}{7}) - \frac{3}{7} lo g_{2} (\frac{3}{7})

- \frac{4}{7} lo g_{2} (\frac{4}{7}) = - lo g_{2} ((\frac{4}{7})^{\frac{4}{7}})

- \frac{3}{7} lo g_{2} (\frac{3}{7}) = - lo g_{2} ((\frac{3}{7})^{\frac{3}{7}})

= - lo g_{2} ((\frac{4}{7})^{\frac{4}{7}}) - lo g_{2} ((\frac{3}{7})^{\frac{3}{7}})

Apply log rule:

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

- lo g_{2} ((\frac{3}{7})^{\frac{3}{7}}) - lo g_{2} ((\frac{4}{7})^{\frac{4}{7}}) = lo g_{2} ((\frac{3}{7})^{\frac{3}{7}} (\frac{4}{7})^{\frac{4}{7}})

= - lo g_{2} ((\frac{3}{7})^{\frac{3}{7}} (\frac{4}{7})^{\frac{4}{7}})

Apply log rule:

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

= - \frac{lo g _{2} ( \frac{27}{7 ^{7}} ) + 8}{7}

lo g_{10} (\frac{5}{36}) - lo g_{10} (\frac{5}{9})

- \frac{1}{44.6} ln (\frac{1}{2})

lo g_{5} (\frac{x}{x + 2})

5 ln (\frac{0.7}{3})

- lo g_{10} (6.4 x 1 0^{- 5})

What is simplify-8/14 log_{2}(8/14)-6/14 log_{2}(6/14) ?
The solution to simplify-8/14 log_{2}(8/14)-6/14 log_{2}(6/14) is -(log_{2}((27)/(7^7))+8)/7