簡約 1/3 log_{2}(3)+2/3 log_{2}(3/2)

解

簡約

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

\frac{lo g _{2} ( \frac{27}{4} )}{3}

十進法表記

0.91829 \dots

解答ステップ

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

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

= \frac{lo g _{2} ( 3 ) + 2 lo g _{2} ( \frac{3}{2} )}{3}

lo g_{2} (3) + 2 lo g_{2} (\frac{3}{2}) = lo g_{2} (\frac{27}{4})

= \frac{lo g _{2} ( \frac{27}{4} )}{3}