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

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

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

simplify

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

lo g_{2} (0.51016 \dots)

Decimal Notation

- 0.97095 \dots

Solution steps

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

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

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

Apply log rule:

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

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

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

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

= lo g_{2} (0.51016 \dots)

lo g_{10} (25) + lo g_{10} (4) + lo g_{10} (2)

lo g_{10} (3) - 2 lo g_{10} (2)

lo g_{3} (405) + lo g_{3} (5)

ln (\frac{1}{2} e^{x})

3 \cdot lo g_{2} (3) - 2 lo g_{2} (5)

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