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

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

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simplify log_{b}((x(x+2)^2)/((x-2)^4))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

2 lo g_{3} (x) + 3 lo g_{3} (y) - 4 lo g_{3} (z)

2 ln (3) - \frac{1}{2} ln (x^{2} + 1)

lo g_{3} (9 x^{2})

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

lo g_{5} (\frac{12 x}{3 y})

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