What is log_{3}((x^2y)/(z^2)) ?

The solution to log_{3}((x^2y)/(z^2)) is 2log_{3}(x)+log_{3}(y)-2log_{3}(z)

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simplify log_{3}((x^2y)/(z^2))

simplify

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

2 lo g_{3} (x) + lo g_{3} (y) - 2 lo g_{3} (z)

Solution steps

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

Apply log rule:

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

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

= lo g_{3} (x^{2} y) - lo g_{3} (z^{2})

lo g_{3} (x^{2} y) = 2 lo g_{3} (x) + lo g_{3} (y)

lo g_{3} (z^{2}) = 2 lo g_{3} (z)

= 2 lo g_{3} (x) + lo g_{3} (y) - 2 lo g_{3} (z)

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

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

ln (e^{- y} \cdot y^{x})

- 8 ln (\frac{1}{2}) + 4

\frac{1}{7} ln (2)

What is log_{3}((x^2y)/(z^2)) ?
The solution to log_{3}((x^2y)/(z^2)) is 2log_{3}(x)+log_{3}(y)-2log_{3}(z)