What is simplify-4/6 log_{2}(4/6)-2/6 log_{2}(2/6) ?

The solution to simplify-4/6 log_{2}(4/6)-2/6 log_{2}(2/6) is log_{2}((\sqrt[3]{3})/(\sqrt[3]{4/9)})

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simplify-4/6 log_{2}(4/6)-2/6 log_{2}(2/6)

simplify

- \frac{4}{6} lo g_{2} (\frac{4}{6}) - \frac{2}{6} lo g_{2} (\frac{2}{6})

Decimal Notation

0.91829 \dots

Solution steps

- \frac{4}{6} lo g_{2} (\frac{4}{6}) - \frac{2}{6} lo g_{2} (\frac{2}{6})

- \frac{4}{6} lo g_{2} (\frac{4}{6}) = - \frac{2}{3} lo g_{2} (\frac{2}{3})

\frac{2}{6} lo g_{2} (\frac{2}{6}) = - \frac{1}{3} lo g_{2} (3)

= - \frac{2}{3} lo g_{2} (\frac{2}{3}) - (- \frac{1}{3} lo g_{2} (3))

Apply rule:

a - (- b) = a + b

- \frac{2}{3} lo g_{2} (\frac{2}{3}) - (- \frac{1}{3} lo g_{2} (3)) = - \frac{2}{3} lo g_{2} (\frac{2}{3}) + \frac{1}{3} lo g_{2} (3)

= - \frac{2}{3} lo g_{2} (\frac{2}{3}) + \frac{1}{3} lo g_{2} (3)

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

\frac{1}{3} lo g_{2} (3) = lo g_{2} (3^{\frac{1}{3}})

= - lo g_{2} ((\frac{2}{3})^{\frac{2}{3}}) + lo g_{2} (3^{\frac{1}{3}})

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{2} (3^{\frac{1}{3}}) - lo g_{2} ((\frac{2}{3})^{\frac{2}{3}}) = lo g_{2} \frac{3 ^{\frac{1}{3}}}{( \frac{2}{3} ) ^{\frac{2}{3}}}

= lo g_{2} \frac{3 ^{\frac{1}{3}}}{( \frac{2}{3} ) ^{\frac{2}{3}}}

Apply exponent rule:

lo g_{5} (6) + lo g_{5} (11)

lo g_{3} (\frac{27}{y})

ln (\frac{e ^{x} - e ^{- x}}{e ^{x} + e ^{- x}})

lo g_{4} (2) + 2 lo g_{4} (5)

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

What is simplify-4/6 log_{2}(4/6)-2/6 log_{2}(2/6) ?
The solution to simplify-4/6 log_{2}(4/6)-2/6 log_{2}(2/6) is log_{2}((\sqrt[3]{3})/(\sqrt[3]{4/9)})