What is log_{3}((81)/(sqrt(x)-9)) ?

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

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simplify log_{3}((81)/(sqrt(x)-9))

simplify

lo g_{3} (\frac{81}{x - 9})

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

Solution steps

lo g_{3} (\frac{81}{x - 9})

Apply log rule:

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

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

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

lo g_{3} (81) = 4

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

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