Solving a logarithmic equation with unlike bases.

Hi guys!

Sorry to dump this one on you without any work done, but I'm really not sure where to start. I've only solved logarithmic equations with like bases so that the one-to-one property is used to eliminate the logarithms.

Here is the equation:

$\displaystyle log_{4}(2x+1) = log_{2}(x-3)-log_{4}(x+5)$

The answer is given as:

$\displaystyle x = \frac{-5+\sqrt{41}}{2}$

Of course, if I'm going to learn anything, I need to see how the correct answer was arrived at. (Itwasntme)

Thanks so much for the help!

Does this logarithmic equation have a solution?