Checking possible answers on a Logarithm problem w/o calc?

[Guest]

Ok suppose I have this example:

The answers are 1/2 or -3.

My teacher told us that we have to know how to check each of the answer in our head or something to figure out the correct one (either 1/2 or -3) without a calculator.

How do I do that?

 

[tkhunny]

You have not changed the Domain in your first step. So let's go with that.

x > -4 -- Both your answers are in there.

The Domain finally changes in your 3rd expression. It will be okay to try the values there. Plug them in.