Question : If $3^{10} × 27^{2}= 9^{2}×3^{n}$, then the value of $n$ is:
Option 1: 10
Option 2: 12
Option 3: 15
Option 4: 30
Answer (1)
24th Jan, 2024
Correct Answer: 12
Solution :
Given: $3^{10} × 27^{2}= 9^{2}×3^{n}$
Simplify the given expression for the same base,
$⇒3^{10} × (3^{3})^{2}= 9^{2}×3^{n}$
$⇒(3^{10+6})= (3^{2})^{2}×3^{n}$
$⇒3^{16}= 3^{4}×3^{n}$
$⇒3^{16}= 3^{4+n}$
By comparing this,
$⇒16=4+n$
$\therefore n =12$
Hence, the correct answer is 12.
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