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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

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

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

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

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

Apply log rule:

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

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

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

lo g_{10} (x^{4}) y^{3}

ln (\frac{2}{8})

lo g_{10} (\frac{x ^{3} y ^{4}}{z ^{5}})

lo g_{b} (3) + 2 lo g_{b} (5)

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