What is log_{3}(x^3\sqrt[5]{y^7}) ?

The solution to log_{3}(x^3\sqrt[5]{y^7}) is 3log_{3}(x)+log_{3}(y)+log_{3}(\sqrt[5]{y^2})

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simplify log_{3}(x^3\sqrt[5]{y^7})

simplify

Solution steps

Simplify

Apply log rule:

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

Simplify

lo g_{3} (x^{3}) : 3 lo g_{3} (x)

lo g_{\frac{1}{4}} (\frac{1}{x}) + 1

lo g_{10} (\frac{x}{7})

ln (x^{\frac{5}{3}}) + ln (y^{4})

lo g_{10} (x^{3}) y^{5}

lo g_{10} (7 x^{4}) + lo g_{10} (9 x^{5})

What is log_{3}(x^3\sqrt[5]{y^7}) ?
The solution to log_{3}(x^3\sqrt[5]{y^7}) is 3log_{3}(x)+log_{3}(y)+log_{3}(\sqrt[5]{y^2})