What is log_{3}((\sqrt[3]{4})/(q^2y)) ?

The solution to log_{3}((\sqrt[3]{4})/(q^2y)) is log_{3}(\sqrt[3]{4})-2log_{3}(q)-log_{3}(y)

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simplify log_{3}((\sqrt[3]{4})/(q^2y))

simplify

Solution steps

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

Simplify

lo g_{3} (q^{2} y) : 2 lo g_{3} (q) + lo g_{3} (y)

Apply the distributive law:

- (a + b) = - a - b

- (2 lo g_{3} (q) + lo g_{3} (y)) = - 2 lo g_{3} (q) - lo g_{3} (y)

lo g_{4} (\frac{x ^{5}}{y ^{8}})

lo g_{2} (3) + lo g_{2} (5) + lo g_{2} (x - 2)

lo g_{10} (x (x^{2} + 2)^{\frac{1}{2}})

ln (x) - 3 [ln (x - 6) + ln (x + 6)]

lo g_{3} (\frac{y}{27})

What is log_{3}((\sqrt[3]{4})/(q^2y)) ?
The solution to log_{3}((\sqrt[3]{4})/(q^2y)) is log_{3}(\sqrt[3]{4})-2log_{3}(q)-log_{3}(y)