Question

Find the number of positive integers which have the characteristic $3$, when the base of the logarithm is $7$.

• A. $2058$
• B. $1029$
• C. $1030$
• D. $2060$

Answer 1

The correct option is A $2058$

Let there be $N$ integers whose characteristic is 3, when base of log is 7
Then, ${\log }_{7}N=x$ where $3\le x<4$
As $3\le x<4$
$3\le {\log }_{7}N<4\Rightarrow 7^3\le N<7^4\Rightarrow N=7^4-7^3\Rightarrow N=2401-343=2058$