What is simplify-(3/4)log_{2}(3/4)-((1/4)log_{2}(1/4)) ?

The solution to simplify-(3/4)log_{2}(3/4)-((1/4)log_{2}(1/4)) is -3/4 log_{2}(3)+2

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simplify-(3/4)log_{2}(3/4)-((1/4)log_{2}(1/4))

simplify

- (\frac{3}{4}) lo g_{2} (\frac{3}{4}) - ((\frac{1}{4}) lo g_{2} (\frac{1}{4}))

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

Decimal Notation

0.81127 \dots

Solution steps

- (\frac{3}{4}) lo g_{2} (\frac{3}{4}) - ((\frac{1}{4}) lo g_{2} (\frac{1}{4}))

Apply rule:

- (a) = - a

- ((\frac{1}{4}) lo g_{2} (\frac{1}{4})) = - (\frac{1}{4}) lo g_{2} (\frac{1}{4})

= - \frac{3}{4} lo g_{2} (\frac{3}{4}) - \frac{1}{4} lo g_{2} (\frac{1}{4})

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

\frac{1}{4} lo g_{2} (\frac{1}{4}) = - \frac{1}{2}

= - \frac{3}{4} (lo g_{2} (3) - 2) - (- \frac{1}{2})

Expand

- \frac{3}{4} (lo g_{2} (3) - 2) - (- \frac{1}{2}) : - \frac{3}{4} lo g_{2} (3) + \frac{4}{2}

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

Divide the numbers:

\frac{4}{2} = 2

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

ln ∣ 3 x + x ∣ - ln (2 - x)

- \frac{5}{2} ln ∣ u + 5 ∣ + \frac{5}{2} ln ∣ u - 5 ∣

lo g_{b} (u^{9} v^{8})

ln (5 e^{5 x})

lo g_{a} (y^{3}) - 3 lo g_{a} (y)

What is simplify-(3/4)log_{2}(3/4)-((1/4)log_{2}(1/4)) ?
The solution to simplify-(3/4)log_{2}(3/4)-((1/4)log_{2}(1/4)) is -3/4 log_{2}(3)+2