What is expand log_{2}((x+3)/(xy)) ?

The solution to expand log_{2}((x+3)/(xy)) is log_{2}(x+3)-log_{2}(x)-log_{2}(y)

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expand log_{2}((x+3)/(xy))

expand

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

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

Solution steps

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

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

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

= lo g_{2} (x + 3) - lo g_{2} (x y)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

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

= lo g_{2} (x + 3) - (lo g_{2} (x) + lo g_{2} (y))

- (lo g_{2} (x) + lo g_{2} (y)) : - lo g_{2} (x) - lo g_{2} (y)

= lo g_{2} (x + 3) - lo g_{2} (x) - lo g_{2} (y)

ln (4 \frac{1}{16})

5 lo g_{6} (x) - 3 lo g_{6} (y)

lo g_{10} (\frac{x}{100})

- lo g_{10} (5 \cdot 1 0^{- 5})

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