What is log_{3}(x^{11}\sqrt[3]{y^4}) ?

The solution to log_{3}(x^{11}\sqrt[3]{y^4}) is 11log_{3}(x)+log_{3}(y)+log_{3}(\sqrt[3]{y})

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simplify log_{3}(x^{11}\sqrt[3]{y^4})

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^{11}) : 11 lo g_{3} (x)

lo g_{10} (\frac{1000}{x ^{2} + y ^{2}})

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

ln (\frac{x ^{2}}{25})

- lo g_{10} (1.3 \cdot 1 0^{- 7})

2 ln (x) - 3 (ln (x^{2}) + ln (x))

What is log_{3}(x^{11}\sqrt[3]{y^4}) ?
The solution to log_{3}(x^{11}\sqrt[3]{y^4}) is 11log_{3}(x)+log_{3}(y)+log_{3}(\sqrt[3]{y})