When to add and when to multiply to find time complexity
You add time complexities when you have something of the form: do operation $A$, then do operation $B$. This would be (time complexity of $A$) + (time complexity of $B$). 

You multiply time complexities when you have something of the form: do operation $A$, $X$ times (eg. in a for loop). This would be $X \cdot $(time complexity of $A$). 

If you perform two binary searches, each of which has time complexity $\log n$, the total runtime is $\log n + \log n$. You might see a runtime of $(\log n)^2$ if you had to perform $\log n$ binary searches.