What is log_{2}((8x^2)/y)+log_{2}(2xy) ?

The solution to log_{2}((8x^2)/y)+log_{2}(2xy) is log_{2}(16x^3)

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simplify log_{2}((8x^2)/y)+log_{2}(2xy)

simplify

lo g_{2} (\frac{8 x ^{2}}{y}) + lo g_{2} (2 x y)

lo g_{2} (16 x^{3})

Solution steps

lo g_{2} (\frac{8 x ^{2}}{y}) + lo g_{2} (2 x y)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{2} (\frac{8 x ^{2}}{y}) + lo g_{2} (2 x y) = lo g_{2} (\frac{8 x ^{2}}{y} \cdot 2 x y)

= lo g_{2} (\frac{8 x ^{2}}{y} \cdot 2 x y)

Simplify

\frac{8 x ^{2}}{y} \cdot 2 x y : 16 x^{3}

= lo g_{2} (16 x^{3})

lo g_{10} (\frac{z ^{5}}{x ^{3} y})

2 lo g_{4} (3) + lo g_{4} (2)

ln (\frac{1}{4 9 ^{k}})

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

lo g_{10} (\frac{a ^{4}}{b ^{5}})

What is log_{2}((8x^2)/y)+log_{2}(2xy) ?
The solution to log_{2}((8x^2)/y)+log_{2}(2xy) is log_{2}(16x^3)