1.

If `(1)/(log_(x)10)=(3)/(log_(p)10)-3`, then x = ______.A. `100p^(2)`B. `(p^(2))/(100)`C. `1000p^(3)`D. `(p^(3))/(1000)`

Answer» Correct Answer - D
Given, `(1)/(log_(x)10) = (3)/(log_(p)10) - 3`
`log_(10)x = 3 log_(10) p - 3 (therefore log_(b) a = (1)/(log_(a)b))`
`log_(10)x = 3(log_(10) p - 1) = 3 (log_(10) p - log_(10) 10)`
`log_(10) x = log_(10) ((p)/(10))^(3)`
`x = ((p)/(10))^(3) = (p^(3))/(1000)`.


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