What is log_{3}(9xy^2)-log_{3}(27xy) ?

The solution to log_{3}(9xy^2)-log_{3}(27xy) is log_{3}(y/3)

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simplify log_{3}(9xy^2)-log_{3}(27xy)

simplify

lo g_{3} (9 x y^{2}) - lo g_{3} (27 x y)

lo g_{3} (\frac{y}{3})

Solution steps

lo g_{3} (9 x y^{2}) - lo g_{3} (27 x y)

Apply log rule:

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

lo g_{3} (9 x y^{2}) - lo g_{3} (27 x y) = lo g_{3} (\frac{9 x y ^{2}}{27 x y})

= lo g_{3} (\frac{9 x y ^{2}}{27 x y})

Cancel

\frac{9 x y ^{2}}{27 x y} : \frac{y}{3}

= lo g_{3} (\frac{y}{3})

lo g_{10} (x y^{2})

ln (\frac{x}{x - 3}) + ln (\frac{x + 3}{x}) - ln (x^{2} - 9)

lo g_{10} (\frac{3}{x})

lo g_{10} (6) - lo g_{10} (3)

What is log_{3}(9xy^2)-log_{3}(27xy) ?
The solution to log_{3}(9xy^2)-log_{3}(27xy) is log_{3}(y/3)