What is log_{b}(x)+2log_{b}(x-2) ?

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

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simplify log_{b}(x)+2log_{b}(x-2)

simplify

lo g_{b} (x) + 2 lo g_{b} (x - 2)

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

Solution steps

lo g_{b} (x) + 2 lo g_{b} (x - 2)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

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

2 ln (x) - \frac{1}{4} ln (y)

lo g_{b} (\frac{x ^{2} y}{z ^{9}})

lo g_{b} (2 y + 5) - \frac{1}{2} lo g_{b} (y + 3)

4 ln (x) - \frac{1}{3} ln (y)

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