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If sqrt((log)2x)-0. 5=(log)2sqrt(x ,) th...

If `sqrt((log)_2x)-0. 5=(log)_2sqrt(x ,)` then `x` equals odd integer (b) prime number composite number (d) irrational

A

odd integer

B

prime number

C

composite number

D

irrational

Text Solution

Verified by Experts

The correct Answer is:
B
`sqrt(log_(2)x)-0.5 = log_(2) sqrtx`
` or sqrt(log_(2)x)-0.5 = 0.5 log_(2)x`
` rArr y - 0.5 = 0.5y^(2)`
`rArr y^(2) - 2y + 1 = 0`
` rArr y = 1`
`rArr log_(2) x = 1`
` rArr x = 2`
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CENGAGE-LOGARITHM AND ITS PROPERTIES-Exercise (Single)
  1. The value of x satisfying sqrt3^(-4+2log(sqrt5)x)= 1//9 is

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  2. The value of x satisfying the equation 3sqrt(5)^(log)5 5^(((log)5(log)...

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  3. If sqrt((log)2x)-0. 5=(log)2sqrt(x ,) then x equals odd integer (b)...

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  4. if (log)y x+(log)x y=1,x^2+y=12 , the value of x y is 9 (b) 12 (c) 15 ...

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  5. 4^(log9 3)+9^(log2 4)=1 0^(logx 83), then x is equal to

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  6. If (x+1)^((log)(10)(x+1))=100(x+1), then

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  7. If log2x+logx2=10/3=log2y+logy2 and x!=y ,then x+y=

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  8. If (log)(10)[1/(2^x+x-1)]=x[(log)(10)5-1] , then x= 4 (b) 3 (c) 2 ...

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  9. If (log)3{5+4(log)3(x-1)}=2, then x is equal to 4 (b) 3 (c) 8 (d) (...

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  10. If 2x^((log)4 3)+3^((log)4x)=27 , then x is equal to 2 (b) 4 (c) 8 (d...

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  11. The equation log4(2-x)+log(0.25)(2+x)=log4(1-x)+log(0.25)(2x+1) has

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  12. The value of b for which the equation 2(log)(1/(25))(b x+28)=-(log)5(1...

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  13. If the equation 2^x+4^y=2^y is solved for y in terms of x where x<0, t...

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  14. The number of solution of x^(log)x(x+3)^2=16 is a)0 (b) 1 (c) 2 (d...

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  15. The product of roots of the equation (log8(8/x^2))/((log8x)^2)=3 is 1 ...

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  16. Let a >1 be a real number. Then the number of roots equation a^(2(log)...

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  17. The number of roots of the equation (log)(3sqrt("x"))x+(log)(3x)sqrt(x...

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  18. The set of all x satisfying the equation x^(log)3x^2+((log)3x)^(2-10)=...

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  19. Number of real values of x satisfying the equation (log)2(x^2-x)(log)...

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  20. Find the value of x satisfying the equations log(3)(log(2)x)+log(1//3)...

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