Respuesta :

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

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