Question

If log 1001= 3.000434, find the number of digits in ${1001}^{101}$

Answer 1

given:

$\Rightarrow \log 1001=3.000434$

multiplying both side by $101$

$\Rightarrow 101\log 1001=101\times 3.000434$

$\Rightarrow \log {1001}^{101}=101\times 3.000434$

$\Rightarrow {1001}^{101}={10}^{101\times 3.000434}$

$\Rightarrow {1001}^{101}={10}^{303.043834}$

(as standard base of $\log$ is $10$)

$\therefore$ No. of digit should be greater than $303$