What is log_{2}(x)-log_{2}(y)-3log_{2}(z) ?

The solution to log_{2}(x)-log_{2}(y)-3log_{2}(z) is log_{2}(x/(yz^3))

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simplify log_{2}(x)-log_{2}(y)-3log_{2}(z)

simplify

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

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

Solution steps

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

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

- 3 lo g_{2} (z) = - lo g_{2} (z^{3})

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= lo g_{2} (\frac{\frac{x}{y}}{z ^{3}})

Simplify

\frac{\frac{x}{y}}{z ^{3}} : \frac{x}{y z ^{3}}

= lo g_{2} (\frac{x}{y z ^{3}})

lo g_{10} (\frac{y ^{4}}{3 x z ^{2}})

lo g_{10} (y) + 6 lo g_{10} (z)

lo g_{4} (\frac{y}{x})

lo g_{5} (7 x)

3 lo g_{5} (x) - \frac{1}{2} lo g_{5} (6 - x)

What is log_{2}(x)-log_{2}(y)-3log_{2}(z) ?
The solution to log_{2}(x)-log_{2}(y)-3log_{2}(z) is log_{2}(x/(yz^3))