What is log_{10}((xy^4)/(z^5)) ?

The solution to log_{10}((xy^4)/(z^5)) is log_{10}(x)+4log_{10}(y)-5log_{10}(z)

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simplify log_{10}((xy^4)/(z^5))

simplify

lo g_{10} (\frac{x y ^{4}}{z ^{5}})

lo g_{10} (x) + 4 lo g_{10} (y) - 5 lo g_{10} (z)

Solution steps

lo g_{10} (\frac{x y ^{4}}{z ^{5}})

Apply log rule:

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

lo g_{10} (\frac{x y ^{4}}{z ^{5}}) = lo g_{10} (x y^{4}) - lo g_{10} (z^{5})

= lo g_{10} (x y^{4}) - lo g_{10} (z^{5})

lo g_{10} (x y^{4}) = lo g_{10} (x) + 4 lo g_{10} (y)

lo g_{10} (z^{5}) = 5 lo g_{10} (z)

= lo g_{10} (x) + 4 lo g_{10} (y) - 5 lo g_{10} (z)

lo g_{5} (A) + lo g_{5} (B)

lo g_{10} (\frac{x}{9})

- lo g_{10} (1.3 \times 1 0^{- 3})

lo g_{10} (\frac{x}{8})

ln (\frac{e ^{2}}{8})

What is log_{10}((xy^4)/(z^5)) ?
The solution to log_{10}((xy^4)/(z^5)) is log_{10}(x)+4log_{10}(y)-5log_{10}(z)