What is log_{2}((xy)/(zt)) ?

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

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simplify log_{2}((xy)/(zt))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

lo g_{2} (z t) = lo g_{2} (z) + lo g_{2} (t)

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

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{2} (z) + lo g_{2} (t)) = - lo g_{2} (z) - lo g_{2} (t)

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

2 ln (x) + 2 ln (x + 2)

lo g_{6} (30) + lo g_{6} (5)

lo g_{2} (5 ab)

lo g_{7} (\frac{x + 8}{5 x - 10})

3.8 + lo g_{10} (\frac{0.48}{0.22})

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