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

The solution to simplify-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})

Rewrite

- 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}) + 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)

lo g_{5} (\frac{u}{v ^{5}})

ln (\frac{7}{9})

ln (\frac{1}{x ^{5}})

lo g_{4} (x y^{8} z^{4})

ln (\frac{11}{8})

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