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

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

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simplify log_{3}((xy^2)/(z^2))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

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

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

lo g_{10} (20) + lo g_{10} (4)

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

ln (4 \frac{1}{16})

5 lo g_{6} (x) - 3 lo g_{6} (y)

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