What is simplify-(5/8)log_{2}(5/8)-(3/8)log_{2}(3/8) ?

The solution to simplify-(5/8)log_{2}(5/8)-(3/8)log_{2}(3/8) is -log_{2}(\sqrt[8]{84375})+3

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simplify-(5/8)log_{2}(5/8)-(3/8)log_{2}(3/8)

simplify

- (\frac{5}{8}) lo g_{2} (\frac{5}{8}) - (\frac{3}{8}) lo g_{2} (\frac{3}{8})

Decimal Notation

0.95443 \dots

Solution steps

- (\frac{5}{8}) lo g_{2} (\frac{5}{8}) - (\frac{3}{8}) lo g_{2} (\frac{3}{8})

Apply rule:

(a) = a

(\frac{5}{8}) = \frac{5}{8}

= - \frac{5}{8} lo g_{2} (\frac{5}{8}) - \frac{3}{8} lo g_{2} (\frac{3}{8})

- \frac{5}{8} lo g_{2} (\frac{5}{8}) = - lo g_{2} ((\frac{5}{8})^{\frac{5}{8}})

- \frac{3}{8} lo g_{2} (\frac{3}{8}) = - lo g_{2} ((\frac{3}{8})^{\frac{3}{8}})

= - lo g_{2} ((\frac{5}{8})^{\frac{5}{8}}) - lo g_{2} ((\frac{3}{8})^{\frac{3}{8}})

Apply log rule:

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

- lo g_{2} ((\frac{3}{8})^{\frac{3}{8}}) - lo g_{2} ((\frac{5}{8})^{\frac{5}{8}}) = lo g_{2} ((\frac{3}{8})^{\frac{3}{8}} (\frac{5}{8})^{\frac{5}{8}})

= - lo g_{2} ((\frac{3}{8})^{\frac{3}{8}} (\frac{5}{8})^{\frac{5}{8}})

Simplify

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{2} (8) = 3

Apply the distributive law:

- (a - b) = - a + b

5 ln (x) + 3 ln (y) - 4 ln (z)

lo g_{10} (6) + lo g_{10} (5) - lo g_{10} (15)

lo g_{10} (\frac{a ^{2}}{b ^{- 3} c ^{4}})

\frac{1}{3} lo g_{b} (x) + 4 lo g_{b} (y) - 3 lo g_{b} (x)

What is simplify-(5/8)log_{2}(5/8)-(3/8)log_{2}(3/8) ?
The solution to simplify-(5/8)log_{2}(5/8)-(3/8)log_{2}(3/8) is -log_{2}(\sqrt[8]{84375})+3