What is log_{10}((x^3sqrt(y))/(z^2)) ?

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

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simplify log_{10}((x^3sqrt(y))/(z^2))

simplify

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

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

Solution steps

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

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

lo g_{10} (x^{3} y) = 3 lo g_{10} (x) + lo g_{10} (y)

lo g_{10} (z^{2}) = 2 lo g_{10} (z)

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

3 ln (3) - 2 ln (2)

ln (x + 1) - ln (x - 4)

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

\frac{8}{3} ln (2)

lo g_{10} ((6 - x) (x + 5))

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