What is simplify-0.2*log_{2}(0.2)-0.8*log_{2}(0.8) ?

The solution to simplify-0.2*log_{2}(0.2)-0.8*log_{2}(0.8) is log_{2}(5)-1.6

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simplify-0.2log_{2}(0.2)-0.8log_{2}(0.8)

simplify

- 0.2 \cdot lo g_{2} (0.2) - 0.8 \cdot lo g_{2} (0.8)

lo g_{2} (5) - 1.6

Decimal Notation

0.72192 \dots

Solution steps

- 0.2 lo g_{2} (0.2) - 0.8 lo g_{2} (0.8)

- 0.2 lo g_{2} (0.2) = 0.2 lo g_{2} (5)

0.8 lo g_{2} (0.8) = 1.6 - 0.8 lo g_{2} (5)

= 0.2 lo g_{2} (5) - (1.6 - 0.8 lo g_{2} (5))

Expand

- (1.6 - 0.8 lo g_{2} (5)) : - 1.6 + 0.8 lo g_{2} (5)

= 0.2 lo g_{2} (5) - 1.6 + 0.8 lo g_{2} (5)

Add similar elements:

0.2 lo g_{2} (5) + 0.8 lo g_{2} (5) = lo g_{2} (5)

= lo g_{2} (5) - 1.6

ln (\frac{k}{2 k})

lo g_{2} (10 x)

\frac{1}{3} lo g_{c} (x) + 5 lo g_{c} (y) - 4 lo g_{c} (x)

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

ln (\frac{6 x ^{2}}{y ^{4}})

What is simplify-0.2*log_{2}(0.2)-0.8*log_{2}(0.8) ?
The solution to simplify-0.2*log_{2}(0.2)-0.8*log_{2}(0.8) is log_{2}(5)-1.6