What is log_{10}((x^5)/(z\sqrt[3]{y^2)}) ?

The solution to log_{10}((x^5)/(z\sqrt[3]{y^2)}) is 5log_{10}(x)-log_{10}(z)-log_{10}(\sqrt[3]{y^2})

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simplify log_{10}((x^5)/(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^{5}) = 5 lo g_{10} (x)

Apply the distributive law:

- (a + b) = - a - b

tanh (\frac{1}{2} ln (\frac{1 + z}{1 - z}))

2 lo g_{10} (2) + 4 lo g_{10} (3)

lo g_{10} (k) - 5 lo g_{10} (g)

lo g_{4} (5 x)

\frac{1}{2} ln (x) - \frac{2}{3} ln (y) - \frac{1}{4} ln (z)

What is log_{10}((x^5)/(z\sqrt[3]{y^2)}) ?
The solution to log_{10}((x^5)/(z\sqrt[3]{y^2)}) is 5log_{10}(x)-log_{10}(z)-log_{10}(\sqrt[3]{y^2})