What is expand log_{10}((xy^3)/(z^2)) ?

The solution to expand log_{10}((xy^3)/(z^2)) is log_{10}(x)+3log_{10}(y)-2log_{10}(z)

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expand log_{10}((xy^3)/(z^2))

expand

lo g_{10} (\frac{x y ^{3}}{z ^{2}})

lo g_{10} (x) + 3 lo g_{10} (y) - 2 lo g_{10} (z)

Solution steps

lo g_{10} (\frac{x y ^{3}}{z ^{2}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{10} (\frac{x y ^{3}}{z ^{2}}) = lo g_{10} (x y^{3}) - lo g_{10} (z^{2})

= lo g_{10} (x y^{3}) - lo g_{10} (z^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= lo g_{10} (x y^{3}) - 2 lo g_{10} (z)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

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

= lo g_{10} (x) + lo g_{10} (y^{3}) - 2 lo g_{10} (z)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= lo g_{10} (x) + 3 lo g_{10} (y) - 2 lo g_{10} (z)

ln (y) - ln (y + 1)

ln (2) - ln (\frac{1}{2})

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

lo g_{b} (\frac{x y ^{4}}{z ^{6}})

What is expand log_{10}((xy^3)/(z^2)) ?
The solution to expand log_{10}((xy^3)/(z^2)) is log_{10}(x)+3log_{10}(y)-2log_{10}(z)