`"If" log_((3x-1))(x-2)= log_((9x^(2)-6x+1))(2x^(2)-10x-2)`, then x equals-

Options

A. `9-sqrt(15)`
B. `3+sqrt(15)`
C. `2+sqrt(5)`
D. `6-sqrt(5)`

Answer

B

Explanation

` log_((3x-1))(x-2)= log_((3x-1))(2x^(2)-10x-2)`
` log_((3x-1))(x-2)^(2)= log_((3x-1))(2x^(2)-10x-2)`
`(x-2)^(2)=2x^(2)-10x-2`
`x^(2)-4x+4=2x^(2)-10x-2`
`x^(2)-6x-6=0`
`x=3+-sqrt(15)`
`x=3-sqrt(15)" "x=3+sqrt(15)`
`at 3-sqrt(15)`
(x-2) is negative