What will be the least integral value of " $n$ " such that $7^{n} > 10^{5}$ , given that ${log}_{10} 343 = 2.5353$ ?

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Solution

The correct option is A 6
$7^{n} > 10^{5}$ iff $n l o g_{10} 7 > 5$
or $n l o g_{10} 7^{3} > 15$ or $n > \frac{15}{2.5353}$
i.e., n > 5.91646.
Hence least such integer $=$ 6

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