The folks at the LA Times have been kind enough to provide a chart showing how much rents have skyrocketed both nationally and in Los Angeles County. They are, as usual, shown in nominal dollars, so I have been kind enough to draw some new lines showing rents in real, inflation-adjusted dollars: Here you go:
Roughly speaking, since 2011 national rents have gone up from $1480 to $1553, an increase of 5 percent. In LA County, rents have gone up from $2,300 to $2,442, an increase of 6 percent. National rents have been flat since about 2015. LA rents have been flat from about 2017.
You may draw your own conclusions from this data.