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

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

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

simplify

Solution steps

Apply log rule:

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

lo g_{10} (z^{3}) = 3 lo g_{10} (z)

Apply the distributive law:

- (a + b) = - a - b

ln (2) - 3 ln (3)

\frac{1}{2} lo g_{c} (x) + 5 lo g_{c} (y) - 2 lo g_{c} (x)

lo g_{5} (x) - lo g_{5} (x^{2})

ln (22)

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