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If P is the number of natural numbers wh...

If P is the number of natural numbers whose logarithms to the base 10 have the the charecteristic p and Q is the numbers of natural numbers logarithms of whose reciprocal to the base 10 have the charecteristics -q. then find the value of `log_(10) P-log_(10) Q`

Text Solution

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`10^p<=p<10^(p+1)`
`p=10^(p+1)-10^p`
`=10^p*q`
`=9.10^p`
Simialrly,
`10^(q-1)ltQ<=10^q`
`Q=10^q-10^(q-1)`
`=9*10^(q-1)`
...
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