Calculate the logarithm to base 9 of 3-4 * 92 * (81)-1
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Correct Answer: Option C
Explanation:
\(3^{-4}\times 9^2 \times 81^{-1}\\
=log_9 (3^{-4}\times 9^2 \times 81^{-1})\\
=log_9 \left(\frac{1}{3^4}\times 9^2 \times \frac{1}{81}\right)\\
=log_9 \left(\frac{1}{81}\times \frac{81}{1}\times \frac{1}{81}\right)\\
=log_9 \frac{1}{81}\\
=log_9 \frac{1}{9^2}\\
=log_9 9^{-2}\\
=-2log_9 9\\
-2 \times 1\\
=-2\)
\(3^{-4}\times 9^2 \times 81^{-1}\\
=log_9 (3^{-4}\times 9^2 \times 81^{-1})\\
=log_9 \left(\frac{1}{3^4}\times 9^2 \times \frac{1}{81}\right)\\
=log_9 \left(\frac{1}{81}\times \frac{81}{1}\times \frac{1}{81}\right)\\
=log_9 \frac{1}{81}\\
=log_9 \frac{1}{9^2}\\
=log_9 9^{-2}\\
=-2log_9 9\\
-2 \times 1\\
=-2\)