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Calculate the logarithm to base 9 of 3^-4 * 9^...

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

A.

2

B.

zero

C.

-2

D.

-4

View answer & explanation

Correct answer is C

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

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