What is 4/10 log_{2}(10/4)+6/10 log_{2}(10/6) ?

The solution to 4/10 log_{2}(10/4)+6/10 log_{2}(10/6) is log_{2}(\sqrt[5]{25/4}\sqrt[5]{125/27})

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simplify 4/10 log_{2}(10/4)+6/10 log_{2}(10/6)

simplify

\frac{4}{10} lo g_{2} (\frac{10}{4}) + \frac{6}{10} lo g_{2} (\frac{10}{6})

Decimal Notation

0.97095 \dots

Solution steps

\frac{4}{10} lo g_{2} (\frac{10}{4}) + \frac{6}{10} lo g_{2} (\frac{10}{6})

\frac{4}{10} lo g_{2} (\frac{10}{4}) = \frac{2}{5} lo g_{2} (\frac{5}{2})

\frac{6}{10} lo g_{2} (\frac{10}{6}) = \frac{3}{5} lo g_{2} (\frac{5}{3})

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

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

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

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

Apply log rule:

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

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

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

- lo g_{10} (1.1 \cdot 1 0^{- 7})

\frac{1}{4} ln (\frac{38}{13})

ln (\frac{e ^{3} x ^{3} x + 2}{3 y ^{2}})

lo g_{10} (8) - lo g_{10} (2) + 2 lo g_{10} (w)

ln (\frac{x ^{3}}{7 y ^{2}})

What is 4/10 log_{2}(10/4)+6/10 log_{2}(10/6) ?
The solution to 4/10 log_{2}(10/4)+6/10 log_{2}(10/6) is log_{2}(\sqrt[5]{25/4}\sqrt[5]{125/27})