What is log_{2}((8x^3)/(2y)) ?

The solution to log_{2}((8x^3)/(2y)) is 2+3log_{2}(x)-log_{2}(y)

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simplify log_{2}((8x^3)/(2y))

simplify

lo g_{2} (\frac{8 x ^{3}}{2 y})

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

Solution steps

lo g_{2} (\frac{8 x ^{3}}{2 y})

Factor the number:

8 = 2 \cdot 4

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

Cancel the common factor:

2

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

Apply log rule:

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

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

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

Simplify

lo g_{2} (4 x^{3}) : 2 + 3 lo g_{2} (x)

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

lo g_{111} (\frac{20000}{111}) + 1

ln (\frac{27027}{625})

\frac{1}{5} ln (y) + ln (z)

2 (ln (x) + ln (3)) - 3 ln (y)

What is log_{2}((8x^3)/(2y)) ?
The solution to log_{2}((8x^3)/(2y)) is 2+3log_{2}(x)-log_{2}(y)