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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

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

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

ln (\frac{125}{27})

ln (\frac{e ^{3}}{3})

ln (\frac{e ^{3}}{4})

ln (y \frac{y}{2 - y})

ln (3) - ln (6)

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