What is 0.5(-3/5 log_{2}(3/5)-2/5 log_{2}(2/5)) ?

The solution to 0.5(-3/5 log_{2}(3/5)-2/5 log_{2}(2/5)) is (-1-0.5log_{2}(27/3125))/5

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simplify 0.5(-3/5 log_{2}(3/5)-2/5 log_{2}(2/5))

simplify

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

\frac{- 1 - 0.5 lo g _{2} ( \frac{27}{3125} )}{5}

Decimal Notation

0.48547 \dots

Solution steps

0.5 (- \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}{5} lo g_{2} (\frac{2}{5}) = \frac{- 3 lo g _{2} ( \frac{3}{5} ) - 2 lo g _{2} ( \frac{2}{5} )}{5}

= 0.5 \cdot \frac{- 3 lo g _{2} ( \frac{3}{5} ) - 2 lo g _{2} ( \frac{2}{5} )}{5}

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

= 0.5 \cdot \frac{- 2 - lo g _{2} ( \frac{27}{3125} )}{5}

0.5 \cdot \frac{- 2 - lo g _{2} ( \frac{27}{3125} )}{5} = \frac{- 1 - 0.5 lo g _{2} ( \frac{27}{3125} )}{5}

= \frac{- 1 - 0.5 lo g _{2} ( \frac{27}{3125} )}{5}

(\frac{( ln ( x ) - ln ( 100 ) )}{2 \cdot ln ( 2 )})^{2}

ln (6) + ln (18) - ln (3) + 3 ln (6)

ln (\frac{100}{5})

100 + 20 \cdot ln (\frac{65}{65 - 30})

20 e^{3 (3)} - ln ∣ 3 - 9 ∣ + 2 ln (3) + 50

What is 0.5(-3/5 log_{2}(3/5)-2/5 log_{2}(2/5)) ?
The solution to 0.5(-3/5 log_{2}(3/5)-2/5 log_{2}(2/5)) is (-1-0.5log_{2}(27/3125))/5