What is expand log_{4}(((1024)/(xy^2))^2) ?

The solution to expand log_{4}(((1024)/(xy^2))^2) is 2(5-log_{4}(xy^2))

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expand log_{4}(((1024)/(xy^2))^2)

expand

lo g_{4} ((\frac{1024}{x y ^{2}})^{2})

2 (5 - lo g_{4} (x y^{2}))

Solution steps

lo g_{4} ((\frac{1024}{x y ^{2}})^{2})

Apply log rule:

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

lo g_{4} ((\frac{1024}{x y ^{2}})^{2}) = 2 lo g_{4} (\frac{1024}{x y ^{2}})

= 2 lo g_{4} (\frac{1024}{x y ^{2}})

Apply log rule:

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

lo g_{4} (\frac{1024}{x y ^{2}}) = lo g_{4} (1024) - lo g_{4} (x y^{2})

= 2 (lo g_{4} (1024) - lo g_{4} (x y^{2}))

lo g_{4} (1024) = 5

= 2 (- lo g_{4} (x y^{2}) + 5)

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

- lo g_{10} (2.7 \cdot 1 0^{- 5})

88.5 ln (\frac{10}{7.4})

ln (5 e^{9})

ln (\frac{10.25 \cdot 1 0 ^{- 12}}{16 \cdot 1 0 ^{- 15}})

What is expand log_{4}(((1024)/(xy^2))^2) ?
The solution to expand log_{4}(((1024)/(xy^2))^2) is 2(5-log_{4}(xy^2))