What is log_{2}((x^2)/(y^6)) ?

The solution to log_{2}((x^2)/(y^6)) is 2log_{2}(x)-6log_{2}(y)

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simplify log_{2}((x^2)/(y^6))

simplify

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

2 lo g_{2} (x) - 6 lo g_{2} (y)

Solution steps

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

Apply log rule:

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

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

= lo g_{2} (x^{2}) - lo g_{2} (y^{6})

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

lo g_{2} (y^{6}) = 6 lo g_{2} (y)

= 2 lo g_{2} (x) - 6 lo g_{2} (y)

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

- \frac{2}{6} lo g_{2} (\frac{2}{6}) - \frac{4}{6} lo g_{2} (\frac{4}{6})

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

ln (\frac{x}{x - 2}) + ln (\frac{x + 2}{x}) - ln (x^{2} - 4)

3 lo g_{10} (x) - 2 lo g_{10} (y)

What is log_{2}((x^2)/(y^6)) ?
The solution to log_{2}((x^2)/(y^6)) is 2log_{2}(x)-6log_{2}(y)