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

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

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

simplify

Solution steps

Apply log rule:

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

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

lo g_{4} (64 x^{5})

ln (x) + 5 ln (y)

ln ((\frac{m ^{5}}{n ^{2}})^{3})

lo g_{8} (10) - 2 lo g_{8} (3)

lo g_{10} (MN)

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