What is log_{2}(8)-log_{2}(x)-log_{2}(y) ?

The solution to log_{2}(8)-log_{2}(x)-log_{2}(y) is log_{2}(8/(xy))

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simplify log_{2}(8)-log_{2}(x)-log_{2}(y)

simplify

lo g_{2} (8) - lo g_{2} (x) - lo g_{2} (y)

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

Solution steps

lo g_{2} (8) - 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} (8) - lo g_{2} (x) = lo g_{2} (\frac{8}{x})

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

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

Simplify

\frac{\frac{8}{x}}{y} : \frac{8}{x y}

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

lo g_{10} (2) + lo g_{10} (3)

lo g_{10} (10 x)

2 lo g_{10} (x) - 3 lo g_{10} (y) + 4 lo g_{10} (z)

lo g_{10} (2 x)

lo g_{3} (2 x)

What is log_{2}(8)-log_{2}(x)-log_{2}(y) ?
The solution to log_{2}(8)-log_{2}(x)-log_{2}(y) is log_{2}(8/(xy))