What is log_{10}((sqrt(x)z)/(y^3)) ?

The solution to log_{10}((sqrt(x)z)/(y^3)) is log_{10}(sqrt(x))+log_{10}(z)-3log_{10}(y)

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simplify log_{10}((sqrt(x)z)/(y^3))

simplify

lo g_{10} (\frac{x z}{y ^{3}})

lo g_{10} (x) + lo g_{10} (z) - 3 lo g_{10} (y)

Solution steps

lo g_{10} (\frac{x z}{y ^{3}})

Apply log rule:

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

lo g_{10} (\frac{x z}{y ^{3}}) = lo g_{10} (x z) - lo g_{10} (y^{3})

= lo g_{10} (x z) - lo g_{10} (y^{3})

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

lo g_{10} (y^{3}) = 3 lo g_{10} (y)

= lo g_{10} (x) + lo g_{10} (z) - 3 lo g_{10} (y)

lo g_{2} (x) - lo g_{2} (x^{2})

lo g_{5} (2) + lo g_{5} (3)

- lo g_{10} (4.1 \times 1 0^{- 4})

ln (\frac{3 + 1}{3 - 1})

What is log_{10}((sqrt(x)z)/(y^3)) ?
The solution to log_{10}((sqrt(x)z)/(y^3)) is log_{10}(sqrt(x))+log_{10}(z)-3log_{10}(y)