What is log_{2}((sqrt(xy))/((z-3)^2)) ?

The solution to log_{2}((sqrt(xy))/((z-3)^2)) is log_{2}(sqrt(xy))-2log_{2}(z-3)

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simplify log_{2}((sqrt(xy))/((z-3)^2))

simplify

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

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

Solution steps

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

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

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

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

Apply log rule:

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

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

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

ln (\frac{x}{x - 2}) + ln (\frac{x + 2}{x}) - ln (x^{2} - 4)

3 lo g_{10} (x) - 2 lo g_{10} (y)

lo g_{5} (\frac{8}{x})

\frac{1}{2} lo g_{7} (x) + lo g_{7} (y)

6 lo g_{b} (q) - lo g_{b} (r)

What is log_{2}((sqrt(xy))/((z-3)^2)) ?
The solution to log_{2}((sqrt(xy))/((z-3)^2)) is log_{2}(sqrt(xy))-2log_{2}(z-3)