Mathematics

Calculate the logarithm to base 9 of 3-4 * 92 * (81)-1

Calculate the logarithm to base 9 of 3-4 * 92 * (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)