What is log_{3}(x^8\sqrt[3]{y^{20}}) ?

The solution to log_{3}(x^8\sqrt[3]{y^{20}}) is 8log_{3}(x)+6log_{3}(y)+log_{3}(\sqrt[3]{y^2})

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simplify log_{3}(x^8\sqrt[3]{y^{20}})

simplify

Solution steps

Simplify

Apply log rule:

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

lo g_{3} (x^{8}) = 8 lo g_{3} (x)

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

8 lo g_{5} (u) + 4 lo g_{5} (v)

lo g_{10} ((4 x)^{5})

- 2 lo g_{b} (x) - 6 lo g_{b} (y) + \frac{1}{7} lo g_{b} (z)

ln ((x^{2} + 1) (x - 1))

What is log_{3}(x^8\sqrt[3]{y^{20}}) ?
The solution to log_{3}(x^8\sqrt[3]{y^{20}}) is 8log_{3}(x)+6log_{3}(y)+log_{3}(\sqrt[3]{y^2})