Question 2
Positive real numbers $b \ne 1$ and $n$ satisfy the equations $$
\sqrt{\log_b n} = \log_b \sqrt{n}
$$ and $$
b \cdot \log_b n = \log_b (bn).
$$ The value of $n$ is $\frac{j}{k},$ where $j$ and $k$ are relatively prime positive integers. Find $j + k.$
\sqrt{\log_b n} = \log_b \sqrt{n}
$$ and $$
b \cdot \log_b n = \log_b (bn).
$$ The value of $n$ is $\frac{j}{k},$ where $j$ and $k$ are relatively prime positive integers. Find $j + k.$