Verified Answer :

RASEA23

If it is log 81 base 1/9=x, then you can make the following equation
(1/9)^x=81
x=-2
in this case since 9 squared is 81 and you need to flip the fraction so you add a negative,
Hope this helps.

Panoyin

\(log_{81}(\frac{1}9})\)
\(81^{x} = \frac{1}{9}\)
\(ln(81^{x}) = ln(\frac{1}{9})\)
\(x\ln(81) = ln(\frac{1}{9})\)
\(\frac{x\ln(81)}{ln(81)} = \frac{ln(\frac{1}{9})}{ln(81)}\)
\(x = \frac{ln(\frac{1}{3})^{2}}{ln(3)^{4}}\)
\(x = \frac{2ln(\frac{1}{3})}{4ln(3)}\)
\(x = \frac{ln(\frac{1}{3})}{2ln(3)}\)
\(x = \frac{-ln(3)}{2ln(3)}\)
\(x = -\frac{1}{2}\)

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