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

If `P`is the number of natural numbers whose logarithms to the base 10

1.	If `P`is the number of natural numbers whose logarithms to the base 10 havethe characteristic `pa n dQ`is the number of natural numbers logarithms of whose reciprocals to thebase 10 have the characteristic `-q`, then find the value of `log_(10)P-(log)_(10)Qdot`
Answer» `10^(p) leP lt 10^(p+1)` ` rArr P=10^(p+1) - 10^(p)` ` rArr P=9 xx 10^(p)` Similarly, `10^(q-1)lt Q le10^(q)` `rArr Q = 10^(q)-10^(q-1) = 10^(q-1)(10-1)=9 xx 10^(q-1)` ` :. log_(10)P-log_(10)Q = log_(10)(P//Q)` ` log_(10)10^(p-q+1)` ` p-q+1`