Calculate the logarithm to base 9 of 3

^{-4}* 9^{2}* (81)^{-1}-
**A.**

2 -
**B.**

zero -
**C.**

-2 -
**D.**

-4

##### Correct Answer: Option C

##### Explanation

(3^{-4}times 9^2 times 81^{-1}\

=log_9 (3^{-4}times 9^2 times 81^{-1})\

=log_9 left(frac{1}{3^4}times 9^2 times frac{1}{81}right)\

=log_9 left(frac{1}{81}times frac{81}{1}times frac{1}{81}right)\

=log_9 frac{1}{81}\

=log_9 frac{1}{9^2}\

=log_9 9^{-2}\

=-2log_9 9\

-2 times 1\

=-2)