What is log_{2}(x)-log_{2}(w)+log_{2}(z) ?

The solution to log_{2}(x)-log_{2}(w)+log_{2}(z) is log_{2}((xz)/w)

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simplify log_{2}(x)-log_{2}(w)+log_{2}(z)

simplify

lo g_{2} (x) - lo g_{2} (w) + lo g_{2} (z)

lo g_{2} (\frac{x z}{w})

Solution steps

lo g_{2} (x) - lo g_{2} (w) + lo g_{2} (z)

Apply log rule:

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

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

= lo g_{2} (\frac{x}{w}) + lo g_{2} (z)

Apply log rule:

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

lo g_{2} (\frac{x}{w}) + lo g_{2} (z) = lo g_{2} (\frac{x}{w} z)

= lo g_{2} (\frac{x}{w} z)

Simplify

\frac{x}{w} z : \frac{x z}{w}

= lo g_{2} (\frac{x z}{w})

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ln (\frac{478}{\frac{212}{13}})

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

What is log_{2}(x)-log_{2}(w)+log_{2}(z) ?
The solution to log_{2}(x)-log_{2}(w)+log_{2}(z) is log_{2}((xz)/w)