What is expand log_{2}((x^3)/(9y)) ?

The solution to expand log_{2}((x^3)/(9y)) is 3log_{2}(x)-2log_{2}(3)-log_{2}(y)

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expand log_{2}((x^3)/(9y))

expand

lo g_{2} (\frac{x ^{3}}{9 y})

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

Solution steps

lo g_{2} (\frac{x ^{3}}{9 y})

Apply log rule:

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

lo g_{2} (\frac{x ^{3}}{9 y}) = lo g_{2} (x^{3}) - lo g_{2} (9 y)

= lo g_{2} (x^{3}) - lo g_{2} (9 y)

Apply log rule:

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

lo g_{2} (x^{3}) = 3 lo g_{2} (x)

= 3 lo g_{2} (x) - lo g_{2} (9 y)

Apply log rule:

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

lo g_{2} (9 y) = lo g_{2} (9) + lo g_{2} (y)

= 3 lo g_{2} (x) - (lo g_{2} (y) + lo g_{2} (9))

lo g_{2} (9) = 2 lo g_{2} (3)

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

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

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

- lo g_{10} (3 \cdot 1 0^{- 9})

ln (1 - x - y) - ln (x)

ln (7) \cdot 0.5 + ln (17) \cdot 0.5

\frac{1}{2} (3 ln (x) - 5 ln (y))

0.0296 (46 e^{(\frac{l n ( 263 ) - l n ( 46 )}{30}) \cdot 1})

What is expand log_{2}((x^3)/(9y)) ?
The solution to expand log_{2}((x^3)/(9y)) is 3log_{2}(x)-2log_{2}(3)-log_{2}(y)