What is log_{b}((y^4\sqrt[3]{x})/(z^5)) ?

The solution to log_{b}((y^4\sqrt[3]{x})/(z^5)) is 4log_{b}(y)+log_{b}(\sqrt[3]{x})-5log_{b}(z)

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simplify log_{b}((y^4\sqrt[3]{x})/(z^5))

simplify

Solution steps

Apply log rule:

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

lo g_{b} (z^{5}) = 5 lo g_{b} (z)

2 ln (x) - ln^{2} (x)

5 lo g_{10} (x) - 2 lo g_{10} (x + 1)

lo g_{10} (x) + lo g_{10} (5) - lo g_{10} (3)

ln (3) - ln (\frac{1}{2})

lo g_{10} (x) + lo g_{10} (\frac{1}{x ^{2}})

What is log_{b}((y^4\sqrt[3]{x})/(z^5)) ?
The solution to log_{b}((y^4\sqrt[3]{x})/(z^5)) is 4log_{b}(y)+log_{b}(\sqrt[3]{x})-5log_{b}(z)