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if 3^(-x) =3000 then find 10^(3)xx3^(2x+...

if `3^(-x) =3000` then find `10^(3)xx3^(2x+3)`.

A

`3xx10^(-3)`

B

`27xx10^(-3)`

C

`9xx10^(-3)`

D

`3000`

Text Solution

Verified by Experts

The correct Answer is:
A
Given ,
`3^(-x)=3000`
`rArr 3^x=(1)/(3000)`
`10^3xx3^(2x+3)=1000xx3^2x xx 3^3`
`=1000 xx3^x xx 3^x xx3^3`
Substituting the value of `3^x` in eq. (2) , we get
`1000xx(1)/(3000)xx(1)/(3000)xx3^3`
`(3)/(1000)=3xx10^(-3)`
Hence, the correct options is (a).
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