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.