What is log_{3}(x^9*\sqrt[3]{y^{17}}) ?

The solution to log_{3}(x^9*\sqrt[3]{y^{17}}) is 9log_{3}(x)+5log_{3}(y)+log_{3}(\sqrt[3]{y^2})

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simplify log_{3}(x^9*\sqrt[3]{y^{17}})

simplify

Solution steps

Simplify

Apply log rule:

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

lo g_{3} (x^{9}) = 9 lo g_{3} (x)

lo g_{3} (y^{5}) = 5 lo g_{3} (y)

ln (x^{2}) - 2 ln (x)

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

lo g_{4} (16 a)

2 lo g_{10} (5) + 5 lo g_{10} (x)

What is log_{3}(x^9*\sqrt[3]{y^{17}}) ?
The solution to log_{3}(x^9*\sqrt[3]{y^{17}}) is 9log_{3}(x)+5log_{3}(y)+log_{3}(\sqrt[3]{y^2})