What is log_{2}((5x^3-2)(x^2-1)^3) ?

The solution to log_{2}((5x^3-2)(x^2-1)^3) is log_{2}(5x^3-2)+3log_{2}(x^2-1)

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simplify log_{2}((5x^3-2)(x^2-1)^3)

simplify

lo g_{2} ((5 x^{3} - 2) (x^{2} - 1)^{3})

lo g_{2} (5 x^{3} - 2) + 3 lo g_{2} (x^{2} - 1)

Solution steps

lo g_{2} ((5 x^{3} - 2) (x^{2} - 1)^{3})

Apply log rule:

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

lo g_{2} ((5 x^{3} - 2) (x^{2} - 1)^{3}) = lo g_{2} (5 x^{3} - 2) + lo g_{2} ((x^{2} - 1)^{3})

= lo g_{2} (5 x^{3} - 2) + lo g_{2} ((x^{2} - 1)^{3})

Apply log rule:

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

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

= lo g_{2} (5 x^{3} - 2) + 3 lo g_{2} (x^{2} - 1)

lo g_{3} (100) - lo g_{3} (18) + lo g_{3} (50)

ln (\frac{( x ^{2} - 1 )}{x ^{5}})

ln (\frac{1}{9 k})

lo g_{b} (z^{5} x)

What is log_{2}((5x^3-2)(x^2-1)^3) ?
The solution to log_{2}((5x^3-2)(x^2-1)^3) is log_{2}(5x^3-2)+3log_{2}(x^2-1)