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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{2} (3 y) = lo g_{2} (3) + lo g_{2} (y)

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

- (lo g_{2} (3) + lo g_{2} (y)) : - lo g_{2} (3) - lo g_{2} (y)

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

\frac{2}{3} lo g_{10} (\frac{x}{1 0 ^{4.4}})

lo g_{2} (5 ab)

4 lo g_{6} (r) - 3 lo g_{6} (s) - 2 lo g_{6} (t)

ln (\frac{2 ^{4}}{3 ^{3} 5 ^{2}})

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