For a positive integer n,the inequality 10^{n | vedclass

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(B) To find the values of $n$ for which $10^{n - 2} > 81n$ holds true,we test integer values starting from $n = 1$:For $n = 1$: $10^{-1} = 0.1$ and $8

Vedclass · Accepted Answer

$n \geq 5$

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(B) To find the values of $n$ for which $10^{n - 2} > 81n$ holds true,we test integer values starting from $n = 1$:For $n = 1$: $10^{-1} = 0.1$ and $81(1) = 81$. $0.1 > 81$ is false.For $n = 2$: $10^{0} = 1$ and $81(2) = 162$. $1 > 162$ is false.For $n = 3$: $10^{1} = 10$ and $81(3) = 243$. $10 > 243$ is false.For $n = 4$: $10^{2} = 100$ and $81(4) = 324$. $100 > 324$ is false.For $n = 5$: $10^{3} = 1000$ and $81(5) = 405$. $1000 > 405$ is true.For $n = 6$: $10^{4} = 10000$ and $81(6) = 486$. $10000 > 486$ is true.Since the inequality holds for $n \geq 5$,the correct option is $B$.

For a positive integer $n$,the inequality $10^{n - 2} > 81n$ holds true if:

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