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

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

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

simplify

Solution steps

Apply log rule:

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

Simplify

ln (2) - ln (\frac{1}{2})

lo g_{10} (x^{2}) - lo g_{10} (x)

lo g_{b} (\frac{x y ^{4}}{z ^{6}})

\frac{1}{3} \cdot ln (64) - ln (12)

5 ln (x - 6) - ln (x^{2} - 11 x + 30) + 2 ln (x - 5)

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