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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

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

lo g_{3} (7) + \frac{1}{2} lo g_{3} (t) - lo g_{3} (r)

\frac{1}{2} \cdot ln (2)

lo g_{10} (\frac{100 x ^{2}}{27})

lo g_{10} (\frac{y}{10000})

2 lo g_{10} (2) + lo g_{10} (3)

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