What is log_{2}(x-1)-3log_{2}(x)-2log_{2}(x+1) ?

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

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simplify log_{2}(x-1)-3log_{2}(x)-2log_{2}(x+1)

simplify

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

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

Solution steps

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

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{\frac{x - 1}{x ^{3}}}{( x + 1 ) ^{2}} : \frac{x - 1}{x ^{3} ( x + 1 ) ^{2}}

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

(0.3)^{2} + 3.2

- (- 8)

\frac{2 3 + 6 3 - 2 3}{2 + 2}

\frac{x - 1}{x + 1}

(- 5 x^{- 3} y^{4})^{2}

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