What is log_{10}((xy^2)/(sqrt(z))) ?

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

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simplify log_{10}((xy^2)/(sqrt(z)))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

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

ln (y e^{x})

- lo g_{10} (4.5 \cdot 1 0^{- 4})

ln (\frac{x ^{2}}{x ( 1 + x ) ^{5}})

lo g_{2} (8 x y)

lo g_{\frac{1}{6}} (\frac{4}{9})

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