"Los Angeles" is more of a concept than a specific place. Los Angeles the city stretches from the San Fernando Valley all the way to the docks at San Pedro, and includes neighborhoods that you'd need a six-figure income to live in and neighborhoods where nobody lives by choice, only because they have no other affordable options.
First thing you need to do is look on a map of the Los Angeles metropolitan area, including everything from the coast on east to neighborhoods out in Pomona, Claremont, Pasadena, and so forth. You need to be very specific about where you want to live before you can even begin to have a ghost of an idea of what it's going to cost you to live.
You also need to understand that "living in Los Angeles" may mean living in a city that is NOT Los Angeles but is in the Los Angeles basin area. For example, I live in the South Bay area of the basin, which includes Redondo Beach, Hermosa Beach, Manhattan Beach, the Palos Verdes Peninsula cities, Torrance, Lomita, San Pedro, Harbor City, and Long Beach. Most people consider those places to be within the "Los Angeles area" but they aren't part of the metropolitan Los Angeles city. And the cost of living varies by quite a lot depending on where you live. For example, Inglewood and Manhattan Beach aren't that far from each other, but are a world away as far as the cost of living.
You also need to factor into your expenses the cost of transportation, because the LA area is so sprawling and spread out that you really do need a car (or motored vehicle of your own of some kind). We don't have very good public transit here and because the area is a patchwork of different cities covered by different transit authorities, it can be very tough to figure out how to route yourself on public transportation and it can take hours to get across the city area because of transfers and waiting for buses or metro. So you need a car and you need to expect to drive, and you need to expect to pay more for gas than in a lot of other places, because anti-smog regulations require a special formulation of gas here that makes it cost more.
So before you even begin to plan a move, you need to do some research to decide, very basically, where in the area you want to move to. Do you want to be near the beach? Near downtown? Near the entertainment industry centers? Do you want to live somewhere on the outskirts, where there's open space, or are you okay with solid urbanization? What kinds of things do you like to do? What kind of work do you want to try to find?
Start by answering those questions, and then you can start to get a feel for how much it will cost and whether your plan is even possible. Good luck.