What is 2/3 log_{2}(x)-3log_{2}(y) ?

The solution to 2/3 log_{2}(x)-3log_{2}(y) is log_{2}((x^{2/3})/(y^3))

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simplify 2/3 log_{2}(x)-3log_{2}(y)

simplify

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

lo g_{2} (\frac{x ^{\frac{2}{3}}}{y ^{3}})

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 lo g_{2} (y) = lo g_{2} (y^{3})

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

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

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

ln (\frac{3 x 1 + 5 x}{( x - 6 ) ^{8}})

ln (\frac{- 1}{2})

lo g_{7} (x y^{3})

- lo g_{10} (4 \times 1 0^{- 3})

ln (3 x)

What is 2/3 log_{2}(x)-3log_{2}(y) ?
The solution to 2/3 log_{2}(x)-3log_{2}(y) is log_{2}((x^{2/3})/(y^3))