What is log_{10}((sqrt(7x))/(y^2)) ?

The solution to log_{10}((sqrt(7x))/(y^2)) is log_{10}(sqrt(7x))-2log_{10}(y)

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simplify log_{10}((sqrt(7x))/(y^2))

simplify

lo g_{10} (\frac{7 x}{y ^{2}})

lo g_{10} (7 x) - 2 lo g_{10} (y)

Solution steps

lo g_{10} (\frac{7 x}{y ^{2}})

Apply log rule:

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

lo g_{10} (\frac{7 x}{y ^{2}}) = lo g_{10} (7 x) - lo g_{10} (y^{2})

= lo g_{10} (7 x) - lo g_{10} (y^{2})

Simplify

lo g_{10} (y^{2}) : 2 lo g_{10} (y)

= lo g_{10} (7 x) - 2 lo g_{10} (y)

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What is log_{10}((sqrt(7x))/(y^2)) ?
The solution to log_{10}((sqrt(7x))/(y^2)) is log_{10}(sqrt(7x))-2log_{10}(y)