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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

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

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

- lo g_{10} (6 \times 1 0^{- 5})

lo g_{10} (5 x + 2) - lo g_{10} (x)

4 lo g_{10} (5) + 1 lo g_{10} (x)

\frac{1}{7} lo g_{3} (5)

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