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If x = "log"(0.1) 0.001, y = "log"(9) 81...

If `x = "log"_(0.1) 0.001, y = "log"_(9) 81`, then `sqrt(x - 2sqrt(y))` is equal to

A

`3-2sqrt(2)`

B

`sqrt(3)-2`

C

`sqrt(2)-1`

D

`sqrt(2)-2`

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`x = "log"_(0.1) 0.001 " and " y = "log"_(9) 81`
`rArr x = "log"_(0.1) (0.1)^(3) " and" y = "log"_(9)9^(2)`
`rArr x = 3 and y = 2`
`therefore sqrt(x-2sqrt(y)) = sqrt(3-2sqrt(2)) = sqrt((sqrt(2)-1)^(2)) = |sqrt(2)-1| = sqrt(2)-1`
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OBJECTIVE RD SHARMA ENGLISH-LOGARITHMS-Chapter Test
  1. If x = "log"(0.1) 0.001, y = "log"(9) 81, then sqrt(x - 2sqrt(y)) is e...

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  2. If x^((3)/(2)("log"(2) x-3)) = (1)/(8), then x equals to

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  3. If "log"(4)(3x^(2) +11x) gt 1, then x lies in the interval

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  4. If "log"(6) (x+3)-"log"(6)x = 2, then x =

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  5. If 2^(x).9^(2x+3) = 7^(x+5), then x =

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  6. The solution of the equation (log)7(log)5(sqrt(x+5)+sqrt(x)=0 is...

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  7. If "log"(6) {"log"(4)(sqrt(x+4) + sqrt(x))} =0, then x =

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  8. If x^("log"(x)(x^(2)-4x +5)) = (x-1), then x =

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  9. If "log"(3) {"log"(6)((x^(2) +x)/(x-1))} =0 then x =

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  10. If "log"(8){"log"(2) "log"(3) (x^(2) -4x +85)} = (1)/(3), then x equal...

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  11. If x = "log"(2) 3 " and " y = "log"(1//2) 5, then

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  12. If "log"(x+2) (x^(3)-3x^(2)-6x +8) =3, then x equals to

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  13. If (2.3)^x=(0.23)^y=1000, then find the value of 1/x-1/y.

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  14. If 10^(x-1) + 10^(-x-1) = (1)/(3), then x equals to

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  15. (log)2(log)2(log)3(log)3 27^3 is 0 b. 1 c. 2 d.\ 3

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  16. If 2"log"(8) a =x, "log"(2) 2a = y " and " y-x =4, then x =

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  17. If "log"(10) x =y, " then log"(10^(3))x^(2) equals

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  18. If "log"(3) x xx "log"(x) 2x xx "log"(2x)y ="log"(x) x^(2), then y equ...

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  19. The number of solutions of "log"(2) (x-1) = 2 "log"(2) (x-3) is

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  20. If (1)/("log"(3) pi) + (1)/("log"(4) pi) gt x, then the greatest integ...

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  21. Let x in(1,oo) and n be a positive integer greater than 1. If fn (x) =...

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