What is log_{10}((\sqrt[3]{z})/(xy^2)) ?

The solution to log_{10}((\sqrt[3]{z})/(xy^2)) is log_{10}(\sqrt[3]{z})-log_{10}(x)-2log_{10}(y)

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simplify log_{10}((\sqrt[3]{z})/(xy^2))

simplify

Solution steps

Apply log rule:

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

Simplify

lo g_{10} (x y^{2}) : lo g_{10} (x) + 2 lo g_{10} (y)

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{10} (x) + 2 lo g_{10} (y)) = - lo g_{10} (x) - 2 lo g_{10} (y)

ln (\frac{e ^{4}}{14})

lo g_{10} (\frac{y}{2})

ln (\frac{5 x}{x ^{2} - 4})

4 ln (x + 1) - 3 ln (y)

ln (\frac{x ^{2} - 4 x + 3}{x ^{2} - 5 x + 6})

What is log_{10}((\sqrt[3]{z})/(xy^2)) ?
The solution to log_{10}((\sqrt[3]{z})/(xy^2)) is log_{10}(\sqrt[3]{z})-log_{10}(x)-2log_{10}(y)