What is log_{2}(16xy^3)-log_{2}(4xy) ?

The solution to log_{2}(16xy^3)-log_{2}(4xy) is log_{2}(4y^2)

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simplify log_{2}(16xy^3)-log_{2}(4xy)

simplify

lo g_{2} (16 x y^{3}) - lo g_{2} (4 x y)

lo g_{2} (4 y^{2})

Solution steps

lo g_{2} (16 x y^{3}) - lo g_{2} (4 x y)

Apply log rule:

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

lo g_{2} (16 x y^{3}) - lo g_{2} (4 x y) = lo g_{2} (\frac{16 x y ^{3}}{4 x y})

= lo g_{2} (\frac{16 x y ^{3}}{4 x y})

Cancel

\frac{16 x y ^{3}}{4 x y} : 4 y^{2}

= lo g_{2} (4 y^{2})

lo g_{a} (x y)

lo g_{10} (16 x)

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

lo g_{8} (\frac{8}{y})

What is log_{2}(16xy^3)-log_{2}(4xy) ?
The solution to log_{2}(16xy^3)-log_{2}(4xy) is log_{2}(4y^2)