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

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

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

simplify

Solution steps

Apply log rule:

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

lo g_{10} (z^{2}) = 2 lo g_{10} (z)

Apply the distributive law:

- (a + b) = - a - b

lo g_{5} (\frac{125}{x + 7})

lo g_{b} (108 b)

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

- 0.9 lo g_{2} (0.9) - 0.1 lo g_{2} (0.1)

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