What is simplify-(3/7)log_{2}(3/7)-(4/7)log_{2}(4/7) ?

The solution to simplify-(3/7)log_{2}(3/7)-(4/7)log_{2}(4/7) is -(log_{2}((27)/(7^7))+8)/7

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simplify-(3/7)log_{2}(3/7)-(4/7)log_{2}(4/7)

simplify

- (\frac{3}{7}) lo g_{2} (\frac{3}{7}) - (\frac{4}{7}) lo g_{2} (\frac{4}{7})

- \frac{lo g _{2} ( \frac{27}{7 ^{7}} ) + 8}{7}

Decimal Notation

0.98522 \dots

Solution steps

- (\frac{3}{7}) lo g_{2} (\frac{3}{7}) - (\frac{4}{7}) lo g_{2} (\frac{4}{7})

Apply rule:

(a) = a

(\frac{3}{7}) = \frac{3}{7}

= - \frac{3}{7} lo g_{2} (\frac{3}{7}) - \frac{4}{7} lo g_{2} (\frac{4}{7})

- \frac{3}{7} lo g_{2} (\frac{3}{7}) = - lo g_{2} ((\frac{3}{7})^{\frac{3}{7}})

- \frac{4}{7} lo g_{2} (\frac{4}{7}) = - lo g_{2} ((\frac{4}{7})^{\frac{4}{7}})

= - lo g_{2} ((\frac{3}{7})^{\frac{3}{7}}) - lo g_{2} ((\frac{4}{7})^{\frac{4}{7}})

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

- lo g_{2} ((\frac{4}{7})^{\frac{4}{7}}) - lo g_{2} ((\frac{3}{7})^{\frac{3}{7}}) = lo g_{2} ((\frac{4}{7})^{\frac{4}{7}} (\frac{3}{7})^{\frac{3}{7}})

= - lo g_{2} ((\frac{4}{7})^{\frac{4}{7}} (\frac{3}{7})^{\frac{3}{7}})

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

= - \frac{lo g _{2} ( \frac{27}{7 ^{7}} ) + 8}{7}

2 ln (2) - ln (5)

ln (\frac{0.6}{0.4})

lo g_{2} (\frac{8 x ^{4}}{5})

4 ln (x) + 2 ln (y) - 6 ln (z)

(85) lo g_{\frac{1}{2}} (\frac{90}{100})

What is simplify-(3/7)log_{2}(3/7)-(4/7)log_{2}(4/7) ?
The solution to simplify-(3/7)log_{2}(3/7)-(4/7)log_{2}(4/7) is -(log_{2}((27)/(7^7))+8)/7