Question

Statement-1 : If `x^("log"_(x) (3-x)^(2)) = 25,` then x =-2
Statement-2: `a^("log"_(a) x) = x,"if" a gt 0, x gt 0 " and " a ne 1`
A. Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True, Statement-2 is true, Statement-2 is NOT a correct explanation for Statement-1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.

Answer 1

Correct Answer - D
`x^("log"_(x)(3-x)^(2)) = 25`
`rArr (3-x)^(2) = 25 " provided that" x gt 0 " and " x ne 1, x ne 3`
`rArr 3-x = +-5 " "[because a^("log"_(a)x) = x]`
`rArr x =-2, x =8`
Hence, statement-2 is true but statement-1 is false.