Find the number of positive integers such that logarithm of whose reciprocals to the base 10 has the characteristic $-2$.

Question

Find the number of positive integers such that logarithm of whose reciprocals to the base 10 has the characteristic $-2$.

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Let $x$ be a positive integer.
Now the characteristic of $\log_{10}(\frac{1}{x})$ is $-2$
I dont know how to solve further.How to count number of positive integers?Please help me.Thanks.

Answer 1

If that is your question, $log_{10} {1/x} = -2$

${1/x} = 10^{-2}$

$x = 100$

does this help?