What is simplify-(1/7)log_{2}(1/7)-(6/7)log_{2}(6/7) ?

The solution to simplify-(1/7)log_{2}(1/7)-(6/7)log_{2}(6/7) is (log_{2}((7^7)/(729))-6)/7

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simplify-(1/7)log_{2}(1/7)-(6/7)log_{2}(6/7)

simplify

- (\frac{1}{7}) lo g_{2} (\frac{1}{7}) - (\frac{6}{7}) lo g_{2} (\frac{6}{7})

\frac{lo g _{2} ( \frac{7 ^{7}}{729} ) - 6}{7}

Decimal Notation

0.59167 \dots

Solution steps

- (\frac{1}{7}) lo g_{2} (\frac{1}{7}) - (\frac{6}{7}) lo g_{2} (\frac{6}{7})

- (\frac{1}{7}) lo g_{2} (\frac{1}{7}) - (\frac{6}{7}) lo g_{2} (\frac{6}{7}) = \frac{1}{7} lo g_{2} (7) - \frac{6}{7} lo g_{2} (\frac{6}{7})

= \frac{1}{7} lo g_{2} (7) - \frac{6}{7} lo g_{2} (\frac{6}{7})

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

- \frac{6}{7} lo g_{2} (\frac{6}{7}) = - lo g_{2} ((\frac{6}{7})^{\frac{6}{7}})

= lo g_{2} (7^{\frac{1}{7}}) - lo g_{2} ((\frac{6}{7})^{\frac{6}{7}})

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{6}{7})^{\frac{6}{7}}) = lo g_{2} \frac{7 ^{\frac{1}{7}}}{( \frac{6}{7} ) ^{\frac{6}{7}}}

= lo g_{2} \frac{7 ^{\frac{1}{7}}}{( \frac{6}{7} ) ^{\frac{6}{7}}}

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}{7} lo g_{2} (\frac{46656}{117649})

\frac{1}{7} lo g_{2} (7) - \frac{1}{7} lo g_{2} (\frac{46656}{117649}) = \frac{lo g _{2} ( 7 ) - lo g _{2} ( \frac{46656}{117649} )}{7}

= \frac{lo g _{2} ( 7 ) - lo g _{2} ( \frac{46656}{117649} )}{7}

lo g_{2} (7) - lo g_{2} (\frac{46656}{117649}) = 7 lo g_{2} (7) - 6 - 6 lo g_{2} (3)

= \frac{7 lo g _{2} ( 7 ) - 6 - 6 lo g _{2} ( 3 )}{7}

7 lo g_{2} (7) - 6 - 6 lo g_{2} (3) = lo g_{2} (\frac{7 ^{7}}{729}) - 6

= \frac{lo g _{2} ( \frac{7 ^{7}}{729} ) - 6}{7}

\frac{1}{3} lo g_{c} (x) + 3 lo g_{c} (y) - 2 lo g_{c} (x)

- lo g_{10} (5.2 \cdot 1 0^{- 8})

3 lo g_{5} (x - 1) - lo g_{5} (3 - 6 x)

ln (x) + ln (x - 4) - 2 ln (x + 1)

What is simplify-(1/7)log_{2}(1/7)-(6/7)log_{2}(6/7) ?
The solution to simplify-(1/7)log_{2}(1/7)-(6/7)log_{2}(6/7) is (log_{2}((7^7)/(729))-6)/7