What is log_{10}(((xy)^2)/(z^3)) ?

The solution to log_{10}(((xy)^2)/(z^3)) is 2log_{10}(x)+2log_{10}(y)-3log_{10}(z)

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simplify log_{10}(((xy)^2)/(z^3))

simplify

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

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

Solution steps

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

Simplify

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

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

Apply log rule:

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

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

= lo g_{10} (x^{2} y^{2}) - lo g_{10} (z^{3})

lo g_{10} (x^{2} y^{2}) = 2 lo g_{10} (x) + 2 lo g_{10} (y)

lo g_{10} (z^{3}) = 3 lo g_{10} (z)

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

ln (\frac{x x - 1}{x ^{2} + 2})

\frac{1}{4} lo g_{b} (x) + 4 lo g_{b} (y) - 2 lo g_{b} (x)

lo g_{b} (\frac{a}{y})

ln (\frac{x}{x + 1})

What is log_{10}(((xy)^2)/(z^3)) ?
The solution to log_{10}(((xy)^2)/(z^3)) is 2log_{10}(x)+2log_{10}(y)-3log_{10}(z)