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

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

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

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

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

Apply log rule:

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

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

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

lo g_{8} (x z^{7})

lo g_{9} (\frac{a}{b ^{2}})

3 lo g_{10} (7) + lo g_{10} (2)

lo g_{7} (49 x)

4 (ln (5) - ln (x)) + (4 ln (x) - ln (25))

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