What is simplify-0.6*log_{2}(0.6)-0.3*log_{2}(0.3) ?

The solution to simplify-0.6*log_{2}(0.6)-0.3*log_{2}(0.3) is -log_{2}(0.51289…)

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simplify-0.6log_{2}(0.6)-0.3log_{2}(0.3)

simplify

- 0.6 \cdot lo g_{2} (0.6) - 0.3 \cdot lo g_{2} (0.3)

- lo g_{2} (0.51289 \dots)

Decimal Notation

0.96326 \dots

Solution steps

- 0.6 lo g_{2} (0.6) - 0.3 lo g_{2} (0.3)

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}) - 0.3 lo g_{2} (0.3)

Apply log rule:

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

0.3 lo g_{2} (0.3) = lo g_{2} (0. 3^{0.3})

= - lo g_{2} (0. 6^{0.6}) - lo g_{2} (0. 3^{0.3})

Rewrite

- lo g_{2} (0. 6^{0.6}) - lo g_{2} (0. 3^{0.3})

- (lo g_{2} (0. 6^{0.6}) + lo g_{2} (0. 3^{0.3}))

= - (lo g_{2} (0. 6^{0.6}) + lo g_{2} (0. 3^{0.3}))

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. 3^{0.3}) = lo g_{2} (0. 6^{0.6} \cdot 0. 3^{0.3})

= - lo g_{2} (0. 6^{0.6} \cdot 0. 3^{0.3})

0. 6^{0.6} \cdot 0. 3^{0.3} = 0.51289 \dots

= - lo g_{2} (0.51289 \dots)

- 4 \cdot ln (\frac{25}{13}) - 5 \cdot ln (\frac{25}{13})

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

\frac{1}{2} ln (\frac{110}{125})

lo g_{8} (\frac{9 x ^{2}}{y ^{3}})

\frac{1}{3} ln (n^{2} + 8) - \frac{1}{3} ln (7 n^{2} + 5)

What is simplify-0.6*log_{2}(0.6)-0.3*log_{2}(0.3) ?
The solution to simplify-0.6*log_{2}(0.6)-0.3*log_{2}(0.3) is -log_{2}(0.51289…)