What is log_{2}((8x^3)/(x^2-1)) ?

The solution to log_{2}((8x^3)/(x^2-1)) is 3+3log_{2}(x)-log_{2}(x^2-1)

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simplify log_{2}((8x^3)/(x^2-1))

simplify

lo g_{2} (\frac{8 x ^{3}}{x ^{2} - 1})

3 + 3 lo g_{2} (x) - lo g_{2} (x^{2} - 1)

Solution steps

lo g_{2} (\frac{8 x ^{3}}{x ^{2} - 1})

Apply log rule:

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

lo g_{2} (\frac{8 x ^{3}}{x ^{2} - 1}) = lo g_{2} (8 x^{3}) - lo g_{2} (x^{2} - 1)

= lo g_{2} (8 x^{3}) - lo g_{2} (x^{2} - 1)

Simplify

lo g_{2} (8 x^{3}) : 3 + 3 lo g_{2} (x)

= 3 + 3 lo g_{2} (x) - lo g_{2} (x^{2} - 1)

lo g_{5} (\frac{f}{125})

lo g_{10} (10 x^{5})

ln (x x^{2} + 5)

lo g_{10} (\frac{1}{x ^{n}})

What is log_{2}((8x^3)/(x^2-1)) ?
The solution to log_{2}((8x^3)/(x^2-1)) is 3+3log_{2}(x)-log_{2}(x^2-1)