My aunt asked me the following question from a teenager she is tutoring:
Given that $\alpha \log \beta + \beta \log \alpha = \frac{1}{5}$, and $\alpha \beta = 10$, what is the value of $\alpha + \beta$?
I was able to derive that $\log \alpha + \log \beta = \log 10$. But this doesn't seem to lead me any closer to the solution.