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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

lo g_{3} (9) = 2

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

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