What is log_{3}((\sqrt[4]{x})/(81y)) ?

The solution to log_{3}((\sqrt[4]{x})/(81y)) is log_{3}(\sqrt[4]{x})-4-log_{3}(y)

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simplify log_{3}((\sqrt[4]{x})/(81y))

simplify

Solution steps

Apply log rule:

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

Simplify

lo g_{3} (81 y) : 4 + lo g_{3} (y)

Apply the distributive law:

- (a + b) = - a - b

- (4 + lo g_{3} (y)) = - 4 - lo g_{3} (y)

lo g_{2} (8 x)

lo g_{10} (10000 y)

ln (6.57 \cdot 1 0^{- 2})

lo g_{7} (2) + lo g_{7} (11)

lo g_{10} (\frac{x ^{3}}{z ^{2} y})

What is log_{3}((\sqrt[4]{x})/(81y)) ?
The solution to log_{3}((\sqrt[4]{x})/(81y)) is log_{3}(\sqrt[4]{x})-4-log_{3}(y)