What is 1/3 log_{2}(3)+2/3 log_{2}(3/2) ?

The solution to 1/3 log_{2}(3)+2/3 log_{2}(3/2) is (log_{2}(27/4))/3

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simplify 1/3 log_{2}(3)+2/3 log_{2}(3/2)

simplify

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

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

Decimal Notation

0.91829 \dots

Solution steps

\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}

lo g_{2} ((r + s) \cdot t)

4 lo g_{10} (x) + 2 lo g_{10} (y)

\frac{1}{3} lo g_{3} (x^{6}) + \frac{1}{6} lo g_{3} (x^{6}) - \frac{1}{9} lo g_{3} (x)

2 ln (x - 1) + 3 ln (x + 1)

lo g_{4} (\frac{4 x ^{6}}{y})

What is 1/3 log_{2}(3)+2/3 log_{2}(3/2) ?
The solution to 1/3 log_{2}(3)+2/3 log_{2}(3/2) is (log_{2}(27/4))/3