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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

simplify

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

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

Decimal Notation

0.81127 \dots

Solution steps

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

Apply rule:

a + (- b) = a - b

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

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

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

Expand

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

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

Divide the numbers:

\frac{4}{2} = 2

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

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

lo g_{2} (x + 7) + lo g_{2} (11 - x)

lo g_{10} (\frac{( 3 b ^{2} + 21 b )}{( 11 b + 77 )})

lo g_{10} (\frac{9 x ^{5}}{y ^{6}})

lo g_{10} (6) - 2 lo g_{10} (y)

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