Positive real numbers b \neq 1 and n satisfy the equations
\sqrt{\log _{b} n}=\log _{b} \sqrt{n} \quad \text { and } \quad b \cdot \log _{b} n=\log _{b}(b n)
The value of n is \frac{j}{k}, where j and k are relatively prime positive integers. Find j+k.