What is 4log_{9}(x)-1/3 log_{9}(y) ?

The solution to 4log_{9}(x)-1/3 log_{9}(y) is log_{9}((x^4y^{2/3})/y)

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simplify 4log_{9}(x)-1/3 log_{9}(y)

simplify

4 lo g_{9} (x) - \frac{1}{3} lo g_{9} (y)

lo g_{9} (\frac{x ^{4} y ^{\frac{2}{3}}}{y})

Solution steps

4 lo g_{9} (x) - \frac{1}{3} lo g_{9} (y)

Apply log rule:

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

4 lo g_{9} (x) = lo g_{9} (x^{4})

= lo g_{9} (x^{4}) - \frac{1}{3} lo g_{9} (y)

Apply log rule:

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

\frac{1}{3} lo g_{9} (y) = lo g_{9} (y^{\frac{1}{3}})

= lo g_{9} (x^{4}) - lo g_{9} (y^{\frac{1}{3}})

Apply log rule:

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

lo g_{9} (x^{4}) - lo g_{9} (y^{\frac{1}{3}}) = lo g_{9} (\frac{x ^{4}}{y ^{\frac{1}{3}}})

= lo g_{9} (\frac{x ^{4}}{y ^{\frac{1}{3}}})

Simplify

\frac{x ^{4}}{y ^{\frac{1}{3}}} : \frac{x ^{4} y ^{\frac{2}{3}}}{y}

= lo g_{9} (\frac{x ^{4} y ^{\frac{2}{3}}}{y})

10 lo g_{3} (x) + 6 lo g_{3} (y)

1 + lo g_{x} (x + 1) - lo g_{x} (x + 4)

lo g_{3} (5 x y)

ln (\frac{i + 1}{i})

What is 4log_{9}(x)-1/3 log_{9}(y) ?
The solution to 4log_{9}(x)-1/3 log_{9}(y) is log_{9}((x^4y^{2/3})/y)