What is expand log_{4}((x^2)/(3y)) ?

The solution to expand log_{4}((x^2)/(3y)) is 2log_{4}(x)-log_{4}(3)-log_{4}(y)

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expand log_{4}((x^2)/(3y))

expand

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

2 lo g_{4} (x) - lo g_{4} (3) - lo g_{4} (y)

Solution steps

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

Apply log rule:

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

lo g_{4} (\frac{x ^{2}}{3 y}) = lo g_{4} (x^{2}) - lo g_{4} (3 y)

= lo g_{4} (x^{2}) - lo g_{4} (3 y)

Apply log rule:

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

lo g_{4} (x^{2}) = 2 lo g_{4} (x)

= 2 lo g_{4} (x) - lo g_{4} (3 y)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{4} (3 y) = lo g_{4} (3) + lo g_{4} (y)

= 2 lo g_{4} (x) - (lo g_{4} (y) + lo g_{4} (3))

- (lo g_{4} (3) + lo g_{4} (y)) : - lo g_{4} (3) - lo g_{4} (y)

= 2 lo g_{4} (x) - lo g_{4} (3) - lo g_{4} (y)

2 lo g_{10} (8) - 4 lo g_{10} (x)

ln (\frac{1.308 x 1 0 ^{- 4}}{6.44 x 1 0 ^{- 3}})

ln (x) - ln (a)

2 ln (x) - ln^{2} (x)

What is expand log_{4}((x^2)/(3y)) ?
The solution to expand log_{4}((x^2)/(3y)) is 2log_{4}(x)-log_{4}(3)-log_{4}(y)