Question

The solution set of `|x+2|^(log_(10)(x^(2)+6x+9))=1` is ______.
A. `{-3, -4}`
B. `{0, -3}`
C. `{-4, -1}`
D. `{-3, -1}`

Answer 1

Correct Answer - C
Given, `|x+2|^(log_(10)x^(2) + 6x+ 9) = 1`
As the RHS = 1
The exponent of x + 2 should be 0 `(a^(0) = 1)` or `|x + 2| = 1`
`implies log_(10) x^(2) + 6x + 9 = 0 or x + 2 = pm 1`
`x^(2) + 6x + 9 = 1 or x = - 1 or - 3`
`x = -2 or -4`
`x = -1 or -3`
when x = -3, `log_(10)(x^(2) + 6x + 9)` is not defined. When x = -2, |x + 2| = 0 which is not possible. x = -4, or -1.