If the equation `x^(log_(a)x^(2))=(x^(k-2))/a^(k),a ne 0`has exactly one solution for x, then the value of k is/areA. `6+4sqrt2`B. `2+6sqrt3)`C. `6-4sqrt2`D. `2-6sqrt3`

If the equation `x^(log_(a)x^(2))=(x^(k-2))/a^(k),a ne 0`has exactly o

1.	If the equation `x^(log_(a)x^(2))=(x^(k-2))/a^(k),a ne 0`has exactly one solution for x, then the value of k is/areA. `6+4sqrt2`B. `2+6sqrt3)`C. `6-4sqrt2`D. `2-6sqrt3`
Answer» Correct Answer - A::C ` (log_(a)x^(2)) log_(a)x =(k-2)log_(a) x - k` (taking log on base a ) Let ` log_(a) x = t`, we get ` 2t^(2) - (k-2) t+k = 0` Putting D= 0 (has only one solution), we have ` (k-2)^(2) - 8k=0` ` or k^(2) - 12k+4 = 0` ` or k=(12 pm sqrt(128))/2` ` or k = 6 pm 4 sqrt2`