Question

Lim extending to zero log to the base sin x into sin 2x

Answer 1

Once you see the solution, you'll get to know by yourself how the solution of this type of questions is to be found out.

In case you don't know anything about the L'Hospital rule, then you simply need to know that it is a differentiation technique which says that you have to differentiate a given function until and unless the indeterminate fom disappears as a solution and it is replaced by a proper answer.