What is log_{10}((x^5sqrt(y))/(z^2)) ?

The solution to log_{10}((x^5sqrt(y))/(z^2)) is 5log_{10}(x)+log_{10}(sqrt(y))-2log_{10}(z)

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simplify log_{10}((x^5sqrt(y))/(z^2))

simplify

lo g_{10} (\frac{x ^{5} y}{z ^{2}})

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

Solution steps

lo g_{10} (\frac{x ^{5} 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 ^{5} y}{z ^{2}}) = lo g_{10} (x^{5} y) - lo g_{10} (z^{2})

= lo g_{10} (x^{5} y) - lo g_{10} (z^{2})

lo g_{10} (x^{5} y) = 5 lo g_{10} (x) + lo g_{10} (y)

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

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

lo g_{5} (\frac{3 y - 8}{y})

ln (\frac{x x - 4}{x ^{5} + 7})

3 ln (x) + 5 ln (y)

lo g_{10} (\frac{6 z}{10})

lo g_{b} (\frac{x y}{z})

What is log_{10}((x^5sqrt(y))/(z^2)) ?
The solution to log_{10}((x^5sqrt(y))/(z^2)) is 5log_{10}(x)+log_{10}(sqrt(y))-2log_{10}(z)