What is log_{4}(x/(z/w)) ?

The solution to log_{4}(x/(z/w)) is log_{4}(x)+log_{4}(w)-log_{4}(z)

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simplify log_{4}(x/(z/w))

simplify

lo g_{4} (\frac{x}{\frac{z}{w}})

lo g_{4} (x) + lo g_{4} (w) - lo g_{4} (z)

Solution steps

lo g_{4} (\frac{x}{\frac{z}{w}})

Simplify

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

= lo g_{4} (\frac{x w}{z})

Apply log rule:

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

lo g_{4} (\frac{x w}{z}) = lo g_{4} (x w) - lo g_{4} (z)

= lo g_{4} (x w) - lo g_{4} (z)

Simplify

lo g_{4} (x w) : lo g_{4} (x) + lo g_{4} (w)

= lo g_{4} (x) + lo g_{4} (w) - lo g_{4} (z)

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What is log_{4}(x/(z/w)) ?
The solution to log_{4}(x/(z/w)) is log_{4}(x)+log_{4}(w)-log_{4}(z)