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

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

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

simplify

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

Decimal Notation

0.91829 \dots

Solution steps

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

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

\frac{4}{6} lo g_{2} (\frac{4}{6}) = \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) = lo g_{2} (3^{\frac{1}{3}})

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

= lo g_{2} (3^{\frac{1}{3}}) - lo g_{2} ((\frac{2}{3})^{\frac{2}{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_{2} (\frac{x y}{( z - 3 ) ^{2}})

ln (\frac{x}{x - 2}) + ln (\frac{x + 2}{x}) - ln (x^{2} - 4)

3 lo g_{10} (x) - 2 lo g_{10} (y)

lo g_{5} (\frac{8}{x})

\frac{1}{2} lo g_{7} (x) + lo g_{7} (y)

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