What is log_{2}((32)/(xy^2)) ?

The solution to log_{2}((32)/(xy^2)) is 5-log_{2}(x)-2log_{2}(y)

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simplify log_{2}((32)/(xy^2))

simplify

lo g_{2} (\frac{32}{x y ^{2}})

5 - lo g_{2} (x) - 2 lo g_{2} (y)

Solution steps

lo g_{2} (\frac{32}{x y ^{2}})

Apply log rule:

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

lo g_{2} (\frac{32}{x y ^{2}}) = lo g_{2} (32) - lo g_{2} (x y^{2})

= lo g_{2} (32) - lo g_{2} (x y^{2})

lo g_{2} (32) = 5

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

= 5 - (lo g_{2} (x) + 2 lo g_{2} (y))

Apply the distributive law:

- (a + b) = - a - b

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

= 5 - lo g_{2} (x) - 2 lo g_{2} (y)

lo g_{10} (\frac{x + 7}{x - 1})

3 ln (x) + 6 ln (y) - 5 ln (z)

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

ln (a b^{t}) - ln ((ab)^{t}) - 2 ln (a)

ln (\frac{7}{6})

What is log_{2}((32)/(xy^2)) ?
The solution to log_{2}((32)/(xy^2)) is 5-log_{2}(x)-2log_{2}(y)