What is simplify-(2/14)log_{2}(2/14)-(3/14)log_{2}(3/14) ?

The solution to simplify-(2/14)log_{2}(2/14)-(3/14)log_{2}(3/14) is (log_{2}(16807/27)+3)/(14)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify-(2/14)log_{2}(2/14)-(3/14)log_{2}(3/14)

simplify

- (\frac{2}{14}) lo g_{2} (\frac{2}{14}) - (\frac{3}{14}) lo g_{2} (\frac{3}{14})

\frac{lo g _{2} ( \frac{16807}{27} ) + 3}{14}

Decimal Notation

0.87727 \dots

Solution steps

- (\frac{2}{14}) lo g_{2} (\frac{2}{14}) - (\frac{3}{14}) lo g_{2} (\frac{3}{14})

- (\frac{2}{14}) lo g_{2} (\frac{2}{14}) - (\frac{3}{14}) lo g_{2} (\frac{3}{14}) = \frac{1}{7} lo g_{2} (7) - \frac{3}{14} lo g_{2} (\frac{3}{14})

= \frac{1}{7} lo g_{2} (7) - \frac{3}{14} lo g_{2} (\frac{3}{14})

\frac{1}{7} lo g_{2} (7) = lo g_{2} (7^{\frac{1}{7}})

- \frac{3}{14} lo g_{2} (\frac{3}{14}) = - lo g_{2} ((\frac{3}{14})^{\frac{3}{14}})

= lo g_{2} (7^{\frac{1}{7}}) - lo g_{2} ((\frac{3}{14})^{\frac{3}{14}})

Apply log rule:

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

lo g_{2} (7^{\frac{1}{7}}) - lo g_{2} ((\frac{3}{14})^{\frac{3}{14}}) = lo g_{2} \frac{7 ^{\frac{1}{7}}}{( \frac{3}{14} ) ^{\frac{3}{14}}}

= lo g_{2} \frac{7 ^{\frac{1}{7}}}{( \frac{3}{14} ) ^{\frac{3}{14}}}

Apply log rule:

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

lo g_{2} (7^{\frac{1}{7}}) = \frac{1}{7} lo g_{2} (7)

= \frac{1}{7} lo g_{2} (7) - \frac{1}{14} lo g_{2} (\frac{27}{2744})

\frac{1}{7} lo g_{2} (7) - \frac{1}{14} lo g_{2} (\frac{27}{2744}) = \frac{- \frac{1}{2} lo g _{2} ( \frac{27}{2744} ) + lo g _{2} ( 7 )}{7}

= \frac{- \frac{1}{2} lo g _{2} ( \frac{27}{2744} ) + lo g _{2} ( 7 )}{7}

- \frac{1}{2} lo g_{2} (\frac{27}{2744}) + lo g_{2} (7) = \frac{- 3 lo g _{2} ( 3 ) + 3 + 5 lo g _{2} ( 7 )}{2}

= \frac{\frac{- 3 l o g _{2} ( 3 ) + 3 + 5 l o g _{2} ( 7 )}{2}}{7}

Apply the fraction rule:

\frac{\frac{a}{b}}{c} = \frac{a}{b \cdot c}

= \frac{- 3 lo g _{2} ( 3 ) + 3 + 5 lo g _{2} ( 7 )}{2 \cdot 7}

Multiply the numbers:

2 \cdot 7 = 14

= \frac{- 3 lo g _{2} ( 3 ) + 3 + 5 lo g _{2} ( 7 )}{14}

- 3 lo g_{2} (3) + 3 + 5 lo g_{2} (7) = lo g_{2} (\frac{16807}{27}) + 3

= \frac{lo g _{2} ( \frac{16807}{27} ) + 3}{14}

lo g_{3} (\frac{9 x ^{4}}{y})

lo g_{m} (a b^{2} c^{3})

lo g_{4} (7) + lo g_{4} (11)

lo g_{3} (27) + lo g_{10} (+ \frac{3}{4})

What is simplify-(2/14)log_{2}(2/14)-(3/14)log_{2}(3/14) ?
The solution to simplify-(2/14)log_{2}(2/14)-(3/14)log_{2}(3/14) is (log_{2}(16807/27)+3)/(14)