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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

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

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

Simplify

lo g_{3} (x^{3}) : 3 lo g_{3} (x)

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

lo g_{2} (\frac{y}{15})

lo g_{9} (5) - lo g_{9} (4)

3 ln (\frac{3}{2})

lo g_{3} (\frac{x}{4})

lo g_{3} (\frac{x}{9})

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