What is simplify-0.6log_{2}(0.6)-0.4log_{2}(0.4) ?

The solution to simplify-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})

Rewrite

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

- (lo g_{2} (0. 6^{0.6}) + 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_{2} (x) - lo g_{2} (y)) + 6 lo g_{2} (z)

lo g_{3} ((7 g^{9} h^{5})^{2})

lo g_{6} (\frac{6}{y})

2 lo g_{b} (x) + 3 lo g_{b} (y)

lo g_{5} (\frac{125}{y})

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