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

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

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simplify log_{2}(x^2-1)-2log_{2}(x-1)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

Simplify

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

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

lo g_{a} (m n^{2})

lo g_{10} ((3 x y z^{2})^{3})

ln (\frac{a ^{- 2} b ^{3}}{c ^{- 5}})

\frac{1}{2} lo g_{2} (13)

lo g_{6} (x \cdot y \cdot z^{5})

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