What is expand log_{3}((27)/(sqrt(x+9))) ?

The solution to expand log_{3}((27)/(sqrt(x+9))) is 3-log_{3}(sqrt(x+9))

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expand log_{3}((27)/(sqrt(x+9)))

expand

lo g_{3} (\frac{27}{x + 9})

3 - lo g_{3} (x + 9)

Solution steps

lo g_{3} (\frac{27}{x + 9})

Apply log rule:

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

lo g_{3} (\frac{27}{x + 9}) = lo g_{3} (27) - lo g_{3} (x + 9)

= lo g_{3} (27) - lo g_{3} (x + 9)

lo g_{3} (27) = 3

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

3 [ln (x - 2) + 2 ln (x + 1) - ln (x + 2) - 5 ln (x - 1)]

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lo g_{10} (100 \cdot x)

- (\frac{3}{5}) lo g_{2} (\frac{3}{5}) - (\frac{2}{5}) lo g_{2} (\frac{2}{5})

(ln^{2} (x) + ln (x) - 2) (lo g_{5} (x - 2))

What is expand log_{3}((27)/(sqrt(x+9))) ?
The solution to expand log_{3}((27)/(sqrt(x+9))) is 3-log_{3}(sqrt(x+9))