If `P` is the number of natural numbers whose logarithms to the base 10 have the characteristic `pa n dQ` is the number of natural numbers logarithms of whose reciprocals to the base 10 have the characteristic `-q` , then find the value of `log_(10)P-(log)_(10)Qdot`

Explanation

To solve the problem, we need to find the values of \( P \) and \( Q \) based on the characteristics of their logarithms, and then compute \( \log_{10} P - \log_{10} Q \).

### Step-by-Step Solution:

1. **Understanding \( P \)**:
- \( P \) is the number of natural numbers whose logarithm to the base 10 has the characteristic \( p \).
- The characteristic of a logarithm is the integer part of the logarithm. Therefore, if \( \log_{10} n \) has a characteristic \( p \), it means:
\[
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