What is log_{3}((\sqrt[3]{2})/(z^2s)) ?

The solution to log_{3}((\sqrt[3]{2})/(z^2s)) is log_{3}(\sqrt[3]{2})-2log_{3}(z)-log_{3}(s)

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simplify log_{3}((\sqrt[3]{2})/(z^2s))

simplify

Solution steps

Apply log rule:

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

Simplify

lo g_{3} (z^{2} s) : 2 lo g_{3} (z) + lo g_{3} (s)

Apply the distributive law:

- (a + b) = - a - b

- (2 lo g_{3} (z) + lo g_{3} (s)) = - 2 lo g_{3} (z) - lo g_{3} (s)

lo g_{5} (\frac{5 x ^{7}}{y})

[ln (x^{5} - 1) - ln (x^{3} - 1)]

- (\frac{4}{6}) lo g_{2} (\frac{4}{6}) - (\frac{2}{6}) lo g_{2} (\frac{2}{6})

ln (\frac{5}{1})

ln (x e^{- x y})

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