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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (x y) + \frac{y + x \frac{d y}{d x}}{y}

lo g_{10} (5 e^{9})

4 lo g_{3} (x) - \frac{1}{2} lo g_{3} (y) + 2 lo g_{3} (z)

1 - ln (2 e)

- \frac{3}{2 ^{44} \cdot 5 ^{44}} ln (10)

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