What is expand log_{6}((\sqrt[3]{x})/(36y^4)) ?

The solution to expand log_{6}((\sqrt[3]{x})/(36y^4)) is log_{6}(\sqrt[3]{x})-2-4log_{6}(y)

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expand log_{6}((\sqrt[3]{x})/(36y^4))

expand

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_{6} (36 y^{4}) = lo g_{6} (36) + lo g_{6} (y^{4})

Apply log rule:

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

lo g_{6} (y^{4}) = 4 lo g_{6} (y)

lo g_{6} (36) = 2

- (2 + 4 lo g_{6} (y)) : - 2 - 4 lo g_{6} (y)

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

ln (x + 2) + ln (x - 2)

ln (3) + \frac{1}{3} ln (8)

3 lo g_{12} (2) + \frac{1}{3} lo g_{12} (8) - lo g_{12} (4)

- lo g_{10} (1.3 \times 1 0^{- 4})

What is expand log_{6}((\sqrt[3]{x})/(36y^4)) ?
The solution to expand log_{6}((\sqrt[3]{x})/(36y^4)) is log_{6}(\sqrt[3]{x})-2-4log_{6}(y)