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

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

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

simplify

Solution steps

Apply log rule:

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

Simplify

lo g_{6} (36 y^{4}) : 2 + 4 lo g_{6} (y)

Apply the distributive law:

- (a + b) = - a - b

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

ln (\frac{x}{3 y})

lo g_{10} (9) + lo g_{10} (5) - lo g_{10} (15)

lo g_{10} (\frac{( a ^{6} b ^{3} )}{c ^{5}})

2 ln (x) + 6 ln (y) - 5 ln (z)

lo g_{3} (6) + lo g_{3} (2)

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