Question

Number of digits in $x^{100}is33$ ( where x > 1), then number of digits in $x^{1000}$ is-

• A. $321$
• B. $300$
• C. $302$
• D. None of these

Answer 1

Answer: (A)

$321$

We know that

${10}^{32}has33digits$

$\therefore {10}^{32}=x^{100}$

take log on both sides,we get

$32=100lo{g}_{10}x$

multiply both sides by $10$,we get

$320=1000lo{g}_{10}x$

take antilog,we get

${10}^{320}=x^{1000}$

$\therefore$, $x^{1000}$ has $321$ digits