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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

lo g_{10} (\frac{y ^{7}}{x z ^{3}})

lo g_{3} (6 x)

ln (\frac{10}{7})

ln (x^{2})

\frac{1}{2} lo g_{4} (x) - 3 lo g_{4} (y) - lo g_{4} (z)

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