Does this logarithmic equation have a solution?

I must solve the following logarithmic equation:

$\displaystyle

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

$

I found the answer as:

$\displaystyle x = \frac{-17\pm\sqrt{305}}{2}$

Which gives me two approximate answers:

0.232 and -17.232

The negative answer clearly cannot be considered a solution. But what about the positive answer? When I sub it back into the original equation, it appears to cause a problem at $\displaystyle log_{2}(x-3)$ since it would give this log a negative argument. However, since it can be converted to $\displaystyle log_{4}(x-3)^2$ does that mean that 0.232 does work as a solution?

Thank you!