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_{10} (a) + 3 lo g_{10} (2 b)

ln (\frac{4}{e})

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

lo g_{b} (4 x) + 7 (lo g_{b} (x) - lo g_{b} (y))

\frac{1}{3} \cdot lo g_{4} (8) + lo g_{4} (15)

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