Here's the equation which I have to solve for x,

$\displaystyle \log_5 (5^{\frac{1}{x}} + 125 ) = \log_5 (6) + 1 + \frac{1}{2x} $

I have tried making the RHS into a single logarithm to the base 5 and then taking anti-log......but that didnt help much.

Please Help.

Thanks in advance