What is log_{2}(x^2y^3)-log_{2}(x)-log_{2}(y) ?

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

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simplify log_{2}(x^2y^3)-log_{2}(x)-log_{2}(y)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

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

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

3 lo g_{10} (x \cdot x^{3})

\frac{1}{2} lo g_{10} (16) - \frac{1}{3} lo g_{10} (8) + 1

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

lo g_{5} (5 x)

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

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