What is 0.4log_{2}(0.4)+0.6log_{2}(0.6) ?

The solution to 0.4log_{2}(0.4)+0.6log_{2}(0.6) is log_{2}(0.51016…)

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simplify 0.4log_{2}(0.4)+0.6log_{2}(0.6)

simplify

0.4 lo g_{2} (0.4) + 0.6 lo g_{2} (0.6)

lo g_{2} (0.51016 \dots)

Decimal Notation

- 0.97095 \dots

Solution steps

0.4 lo g_{2} (0.4) + 0.6 lo g_{2} (0.6)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

0.4 lo g_{2} (0.4) = lo g_{2} (0. 4^{0.4})

= lo g_{2} (0. 4^{0.4}) + 0.6 lo g_{2} (0.6)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

0.6 lo g_{2} (0.6) = lo g_{2} (0. 6^{0.6})

= lo g_{2} (0. 4^{0.4}) + lo g_{2} (0. 6^{0.6})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{2} (0. 4^{0.4}) + lo g_{2} (0. 6^{0.6}) = lo g_{2} (0. 4^{0.4} \cdot 0. 6^{0.6})

= lo g_{2} (0. 4^{0.4} \cdot 0. 6^{0.6})

0. 4^{0.4} \cdot 0. 6^{0.6} = 0.51016 \dots

= lo g_{2} (0.51016 \dots)

4 \cdot ln (\frac{1}{2})

\frac{1}{2} ln (tan (\frac{x}{2}))

ln (\frac{- a}{2 b - a}) - ln (- 1)

- 8267 ln (\frac{0.07}{100})

What is 0.4log_{2}(0.4)+0.6log_{2}(0.6) ?
The solution to 0.4log_{2}(0.4)+0.6log_{2}(0.6) is log_{2}(0.51016…)