What is simplify-0.6*log_{2}(0.6)-(1-0.6)*log_{2}(1-0.6) ?

The solution to simplify-0.6*log_{2}(0.6)-(1-0.6)*log_{2}(1-0.6) is -log_{2}(0.51016…)

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simplify-0.6log_{2}(0.6)-(1-0.6)log_{2}(1-0.6)

simplify

- 0.6 \cdot lo g_{2} (0.6) - (1 - 0.6) \cdot lo g_{2} (1 - 0.6)

- lo g_{2} (0.51016 \dots)

Decimal Notation

0.97095 \dots

Solution steps

- 0.6 lo g_{2} (0.6) - (1 - 0.6) lo g_{2} (1 - 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. 6^{0.6}) - lo g_{2} (1 - 0.6) (1 - 0.6)

Apply log rule:

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

lo g_{2} (1 - 0.6) (1 - 0.6) = lo g_{2} ((1 - 0.6)^{(1 - 0.6)})

= - lo g_{2} (0. 6^{0.6}) - lo g_{2} ((1 - 0.6)^{(1 - 0.6)})

Rewrite

- lo g_{2} (0. 6^{0.6}) - lo g_{2} ((1 - 0.6)^{(1 - 0.6)})

- (lo g_{2} (0. 6^{0.6}) + lo g_{2} ((1 - 0.6)^{(1 - 0.6)}))

= - (lo g_{2} (0. 6^{0.6}) + lo g_{2} ((1 - 0.6)^{(1 - 0.6)}))

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} ((1 - 0.6)^{(1 - 0.6)}) = lo g_{2} (0. 6^{0.6} (1 - 0.6)^{1 - 0.6})

= - lo g_{2} (0. 6^{0.6} (1 - 0.6)^{1 - 0.6})

0. 6^{0.6} (1 - 0.6)^{(1 - 0.6)} = 0.51016 \dots

= - lo g_{2} (0.51016 \dots)

lo g_{\frac{0.25}{450}} (- 2 lo g_{4.5} (x))

- lo g_{10} (5.27 \cdot 1 0^{- 6})

10 lo g_{10} (\frac{1}{86400} 1 0^{\frac{115}{10}})

\frac{1}{8} ln (\frac{22}{- 4})

ln (e^{\frac{n y B}{k T}} (1 + e^{- \frac{2 y B}{k T}})^{n})

What is simplify-0.6*log_{2}(0.6)-(1-0.6)*log_{2}(1-0.6) ?
The solution to simplify-0.6*log_{2}(0.6)-(1-0.6)*log_{2}(1-0.6) is -log_{2}(0.51016…)