You have a misunderstanding here.
Louisiana purchased nothing, the US purchased the territory that France identified as Louisiana which was much larger than the modern state of Louisiana. French Louisiana included all lands west of the Mississippi river except the southwest (claimed by Spain) and the Pacific northwest (claimed by England and Russia). However the precise boundaries of the Louisiana Purchase were (and still are) uncertain.
The Louisiana Purchase
the spanish had control of the mississippi river in 1764
The Louisiana Purcahse gave the U.S access to the port of the Mississippi River and more land out west doubling their size.
Before the Louisiana purchase the French controlled all land west of the Mississippi river. Later in the century a deal was struck between the US and the Russians to buy the territory that is now know as Alaska.
lands west of the Mississippi that were owned by the French
The Louisiana Territory/The Louisiana Purchase
The Louisiana Purchase
the spanish had control of the mississippi river in 1764
The Louisiana Purcahse gave the U.S access to the port of the Mississippi River and more land out west doubling their size.
Before the Louisiana purchase the French controlled all land west of the Mississippi river. Later in the century a deal was struck between the US and the Russians to buy the territory that is now know as Alaska.
lands west of the Mississippi that were owned by the French
The Louisiana purchase was a land deal between the United States and France, in which the U.S. acquired approximately 827,000 square miles of land west of the Mississippi River for $15 million dollars.
The Louisiana Purchase was about the westward expansion of the new United States. It was purchased from France in 1803 and amounted to 800,000 square miles of new land.
The Louisiana Purchase.
Many people explored the land west of the Mississippi, but it seems most likely the question is asking about just after the Louisiana Purchase, if so then the answer is Louis and Clark. However if that is not the answer you are looking for you must resubmit the question with more specificity.
The strip of land that the united states thought was in the Louisiana purchase but wasn't was West Florida.
The Louisiana Purchase was the land west of the Mississippi River that was bought from Napoleon while he was trying to take over Europe. Lewis and Clark went out on a mission across the Louisiana Purchase to find the Northwest Passage. (There mission was a failure, since there was no Northwest Passage).