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

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

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

simplify

Solution steps

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{b} (x^{4} y^{4}) = lo g_{b} (x^{4}) + lo g_{b} (y^{4})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{b} (x^{4}) = 4 lo g_{b} (x)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{b} (y^{4}) = 4 lo g_{b} (y)

- (4 lo g_{b} (x) + 4 lo g_{b} (y)) : - 4 lo g_{b} (x) - 4 lo g_{b} (y)

lo g_{5} (4) + lo g_{5} (9)

\frac{1}{5800} ln (\frac{1}{2})

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

ln (\frac{x}{y ^{5} z})

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

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