Question:
If \(81^2 \div 3^4 = 3^n\), find the value of \(n\).
यदि \(81^2 \div 3^4 = 3^n\) है, तो \(n\) का मान ज्ञात कीजिए।
Options:
- 4
- 6
- 8
- 10
- 4
- 6
- 8
- 10
Correct Answer: a)
Explanation:
Express 81 in base 3:
\(81 = 3^4 \implies 81^2 = (3^4)^2 = 3^8\).
Now, \(81^2 \div 3^4 = 3^8 \div 3^4 = 3^{8-4} = 3^4\).
Comparing powers with \(3^n\): \(n = 4\).
\(81 = 3^4 \implies 81^2 = (3^4)^2 = 3^8\).
\(3^8 \div 3^4 = 3^{8 – 4} = 3^4 = 3^n \implies n = 4\)। अतः विकल्प (a) सही है।