The approximate value of the expression $2\log_3 3n - \log_3(n^2 + 1)$ for a sufficiently large $n$ is

Question and options

The approximate value of the expression

2\log_3 3n - \log_3(n^2 + 1)

for a sufficiently large

n

2
3
$2 - \log_3 2$
1

Answer and explanation

Correct answer: A - 2

2 log3(3n) - log3(n^2+1) = log3(9n^2/(n^2+1)), which tends to log3(9) = 2 for large n. The ratio n^2/(n^2+1) approaches 1 from below, so the value settles at 2 rather than at 3 or at 2 - log3 2.

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The approximate value of the expression \(2\log_3 3n - \log_3(n^2 + 1)\) for a sufficiently large \(n\) is