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

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

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simplify log_{2}(xy)-log_{2}(x^2)

simplify

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

lo g_{2} (\frac{y}{x})

Solution steps

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

Apply log rule:

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

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

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

Simplify

\frac{x}{x ^{2}} : \frac{1}{x}

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

lo g_{3} (x) + lo g_{3} (x + 6)

ln (y \frac{x}{z})

lo g_{10} (\frac{5 x}{7 - x})

lo g_{4} (16 a)

2 lo g_{10} (x) + lo g_{10} (5)

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