Suppose that $B$ is a standard Brownian motion and $b$ is a bounded, measurable function. Using the Girsanov theorem, construct a solution to the SDE $$dX_t=b(X_t)dt+dB_t.$$
I really don't know where to start with this, as I'm not sure how a change of measure could be used for a solution. Any advice would be greatly appreciated! Thanks!