What is log_{3}(x^5\sqrt[3]{y^{19}}) ?

The solution to log_{3}(x^5\sqrt[3]{y^{19}}) is 5log_{3}(x)+6log_{3}(y)+log_{3}(\sqrt[3]{y})

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simplify log_{3}(x^5\sqrt[3]{y^{19}})

simplify

Solution steps

Simplify

Apply log rule:

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

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

lo g_{3} (y^{6}) = 6 lo g_{3} (y)

7 ln (219) + 18 - 7 ln (3) + 6

lo g_{10} (\frac{9 z}{6})

lo g_{10} (\frac{0.402}{0.37}) + 6.247

lo g_{b} (x z^{3})

lo g_{3} (16) - 2 \cdot lo g_{3} (x) + 2 \cdot lo g_{3} (y)

What is log_{3}(x^5\sqrt[3]{y^{19}}) ?
The solution to log_{3}(x^5\sqrt[3]{y^{19}}) is 5log_{3}(x)+6log_{3}(y)+log_{3}(\sqrt[3]{y})