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If `p , q in N` satisfy the equation `x^x=(sqrt(x))^2,` then `pa n dq` are relatively prime (b) twin prime (c) coprime if `(log)_q p` is defined, then `(log)_p q` is not and vice versa

A

p+q=5

B

`|p-q|=4`

C

pq=4

D

if ` log_(q) p ` is defined, then ` log_(p)q ` is not and vice versa

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
` x ^(sqrtx)=(sqrtx)^(x) ,p,qinN`
`rArr sqrtx log x = x log sqrtx`
` or log x [sqrtx - x/2] = 0`
` rArr log x = 0 or [sqrtx - x/2] = 0`
` rArr x = 1 or 4`
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CENGAGE-LOGARITHM AND ITS PROPERTIES-Exercise (Multiple)
  1. For a >0,!=1, the roots of the equation (log)(a x)a+(log)x a^2+(log)(a...

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  2. The real solutions of the equation 2^(x+2). 5^(6-x)=10^x^2 is/are 1 (b...

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  3. If (logx)/(b-c)=(logy)/(c-a)=(logz)/(a-b) , then which of the followin...

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  4. If (log)k xdot(log)5k=(log)x5,k!=1,k >0, then x is equal to k (b) 1/5...

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  5. If p , q in N satisfy the equation x^x=(sqrt(x))^2, then pa n dq are ...

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  6. Which of the following, when simplified, reduces to unity? (log)(10)5...

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  7. If (log)a x=b for permissible values of aa n dx , then identify the st...

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  8. The number of solutions of the equation log(x+1)(x-0.5)=log(x-0.5)(x+1...

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  9. The equation sqrt(1+log(x) sqrt27) log(3) x+1 = 0 has

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  10. If log(1//2)(4-x)gelog(1//2)2-log(1//2)(x-1),then x belongs to

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  11. If the equation x^(log(a)x^(2))=(x^(k-2))/a^(k),a ne 0has exactly one ...

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  12. The set of real values of x satisfying the equation |x-1|^(log3(x^2)-...

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  13. If x = 9 is one of the solutions of log(e)(x^(2)+15a^(2))-log(e)(a...

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  14. In which of the following, m gt n (m,n in R)?

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  15. if log10 5=a and log10 3=b then:

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  16. The value of (6 a^(log(e)b)(log(a^(2))b)(log(b^(2))a))/(e^(log(e)a*lo...

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  17. The inequality sqrt(x^((log)2sqrt(x)))geq2 is satisfied by (A) only on...

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