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The equation sqrt(1+log(x) sqrt27) log...

The equation ` sqrt(1+log_(x) sqrt27) log_(3) x+1 = 0` has

A

no integral solution

B

one irrational solution

C

two real solutions

D

no prime solution

Text Solution

Verified by Experts

The correct Answer is:
A, D
` (sqrt(1+3/(2log_(3)x))) log_(3) x +1 = 0`
Let ` log_(3) x = y" we get "`
`(sqrt(1+3/(2y)))y =- 1`
` or (1+3/(2y)) = 1/y^(2)`
` or (2y+3)/(2y)= 1/y^(2)`
` or 2y^(2) + 3y-2= 0 (.:' y ne 0)`
` or 2y^(2) + 4y-y - 2 = 0`
` or (y+2)(2y-1)=0`
` y = 1//2 or y =- 2 ` (not possible)
` rArr x = 3^(1//2)`
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