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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

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

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

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

ln (2 e^{3})

ln (e^{2} x)

ln (\frac{x ^{3} y ^{2}}{z ^{5}})

ln (2 a) - ln (a)

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