What is simplify-(2/5 log_{2}(2/5)+3/5 log_{2}(3/5)) ?

The solution to simplify-(2/5 log_{2}(2/5)+3/5 log_{2}(3/5)) is -(2+log_{2}(27/3125))/5

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simplify-(2/5 log_{2}(2/5)+3/5 log_{2}(3/5))

simplify

- (\frac{2}{5} lo g_{2} (\frac{2}{5}) + \frac{3}{5} lo g_{2} (\frac{3}{5}))

- \frac{2 + lo g _{2} ( \frac{27}{3125} )}{5}

Decimal Notation

0.97095 \dots

Solution steps

- (\frac{2}{5} lo g_{2} (\frac{2}{5}) + \frac{3}{5} lo g_{2} (\frac{3}{5}))

\frac{2}{5} lo g_{2} (\frac{2}{5}) + \frac{3}{5} lo g_{2} (\frac{3}{5}) = \frac{2 lo g _{2} ( \frac{2}{5} ) + 3 lo g _{2} ( \frac{3}{5} )}{5}

= - \frac{2 lo g _{2} ( \frac{2}{5} ) + 3 lo g _{2} ( \frac{3}{5} )}{5}

2 lo g_{2} (\frac{2}{5}) + 3 lo g_{2} (\frac{3}{5}) = 2 + lo g_{2} (\frac{27}{3125})

= - \frac{2 + lo g _{2} ( \frac{27}{3125} )}{5}

ln (\frac{9}{25})

ln (x) + \frac{1}{2} ln (y) + ln (\frac{1}{2}) z

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

lo g_{10} (5) - lo g_{10} (y) - lo g_{10} (9 c)

7 (lo g_{10} (x) - lo g_{10} (y))

What is simplify-(2/5 log_{2}(2/5)+3/5 log_{2}(3/5)) ?
The solution to simplify-(2/5 log_{2}(2/5)+3/5 log_{2}(3/5)) is -(2+log_{2}(27/3125))/5