Question

If '$n$' is a natural number $>1$, then the least value of "$n$" for which ${\log }_{n}121<3.8$ would be:

• A. 4
• B. 11
• C. 121
• D. 13

Answer 1

The correct option is A 4

Given ${\log }_{n}121<3.8$

$\therefore 121<n^{3.8}$

Taking $\log$ of base $10$ on both sides.

$3.8{\log }_{10}n>{\log }_{10}121$,

${\log }_{10}n>\frac{{\log }_{10}121}{3.8}$

or ${\log }_{10}n>0.5481$,

$n>{10}^{0.5481}$

We get $n>3.5327$

$\therefore$ least integral value of $n=4$