Logs: What is b/a?

This isn't a homework question. I just want to know how to do this out of curiosity. It looks like something my teacher would put on a quiz, lol.
http://img228.imageshack.us/img228/1799/untitled8av.png

You need to find such that

Now looking at the first part of the equation

For these to be equal and , are there any other values that work?

but does this hold for the third part of the equation?

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