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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

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

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

3 lo g_{10} (x) - 4 lo g_{10} (y)

lo g_{2} (\frac{6 x}{y})

lo g_{10} (\frac{10}{0.1})

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