What is expand log_{2}(((x-4)^2)/x) ?

The solution to expand log_{2}(((x-4)^2)/x) is 2log_{2}(x-4)-log_{2}(x)

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expand log_{2}(((x-4)^2)/x)

expand

lo g_{2} (\frac{( x - 4 ) ^{2}}{x})

2 lo g_{2} (x - 4) - lo g_{2} (x)

Solution steps

lo g_{2} (\frac{( x - 4 ) ^{2}}{x})

Apply log rule:

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

lo g_{2} (\frac{( x - 4 ) ^{2}}{x}) = lo g_{2} ((x - 4)^{2}) - lo g_{2} (x)

= lo g_{2} ((x - 4)^{2}) - lo g_{2} (x)

Apply log rule:

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

lo g_{2} ((x - 4)^{2}) = 2 lo g_{2} (x - 4)

= 2 lo g_{2} (x - 4) - lo g_{2} (x)

3 ln (x) + 3 ln (y)

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

lo g_{16} (\frac{4 x ^{5}}{z})

(- \frac{4}{6}) lo g_{2} (\frac{4}{6}) - (\frac{2}{6}) lo g_{2} (\frac{2}{6})

lo g_{8} (x z^{7})

What is expand log_{2}(((x-4)^2)/x) ?
The solution to expand log_{2}(((x-4)^2)/x) is 2log_{2}(x-4)-log_{2}(x)