What is log_{3}((81sqrt(x))/(x^2+9)) ?

The solution to log_{3}((81sqrt(x))/(x^2+9)) is 4+log_{3}(sqrt(x))-log_{3}(x^2+9)

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simplify log_{3}((81sqrt(x))/(x^2+9))

simplify

lo g_{3} (\frac{81 x}{x ^{2} + 9})

4 + lo g_{3} (x) - lo g_{3} (x^{2} + 9)

Solution steps

lo g_{3} (\frac{81 x}{x ^{2} + 9})

Apply log rule:

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

lo g_{3} (\frac{81 x}{x ^{2} + 9}) = lo g_{3} (81 x) - lo g_{3} (x^{2} + 9)

= lo g_{3} (81 x) - lo g_{3} (x^{2} + 9)

Simplify

lo g_{3} (81 x) : 4 + lo g_{3} (x)

= 4 + lo g_{3} (x) - lo g_{3} (x^{2} + 9)

f (z) = lo g_{2} (\frac{z}{4})

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What is log_{3}((81sqrt(x))/(x^2+9)) ?
The solution to log_{3}((81sqrt(x))/(x^2+9)) is 4+log_{3}(sqrt(x))-log_{3}(x^2+9)