Originally Posted by
ILikeSerena Hi rcs!
This is incorrect.
When the base of the log is between 0 and 1 the inequality swaps around.
The last step is incorrect.
If x would be smaller than -4, say -5, then both factors are negative, resulting in a positive number.
Note that a product is negative, if and only if the factors have opposite signs.
Btw, are you aware that you cannot take the log of zero or a negative number?
That is, you have the additional constraint that x^2+ 4x +3 > 0.
It means that when you have solved your inequality, you need to verify that this constraint is satisfied.