What is log_{10}((x^7)/(z\sqrt[3]{y^2)}) ?

The solution to log_{10}((x^7)/(z\sqrt[3]{y^2)}) is 7log_{10}(x)-log_{10}(z)-log_{10}(\sqrt[3]{y^2})

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simplify log_{10}((x^7)/(z\sqrt[3]{y^2)})

simplify

Solution steps

Apply log rule:

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

lo g_{10} (x^{7}) = 7 lo g_{10} (x)

Apply the distributive law:

- (a + b) = - a - b

ln (\frac{x}{3})

ln (\frac{x}{4})

lo g_{4} (6) + 2 lo g_{4} (7)

2 lo g_{5} (12) - lo g_{5} (8) - 2 lo g_{5} (3)

What is log_{10}((x^7)/(z\sqrt[3]{y^2)}) ?
The solution to log_{10}((x^7)/(z\sqrt[3]{y^2)}) is 7log_{10}(x)-log_{10}(z)-log_{10}(\sqrt[3]{y^2})