MonoGame - RenderTarget2D drawn below sprites and in the wrong location

This seems like a simple thing but still doesn't work. So I'm trying to draw a scrollable log window (not scrolling yet) by using a RenderTarget2D.

There are several bugs:

The text should be drawn on a black background, now it seems transparent
The text should be drawn in the black box below the game area, now it's drawn in the top left corner
The text appears now on the background color only, it should be drawn over the other sprites

What's wrong with my code? The relevant parts are below.

    private GraphicsDevice graphicsDevice;
    private RenderTarget2D logRenderTarget;

    private bool redrawLogFlag;

    public void Init(ContentManager content, GraphicsDevice graphicsDevice)
    {
        this.graphicsDevice = graphicsDevice;
        logRenderTarget = new RenderTarget2D(
            graphicsDevice,
            10,
            10
        );
        Log.LogWritten += SetRedrawLogFlag;
    }

    private void DrawUiComponents(SpriteBatch spriteBatch)
    {
        spriteBatch.Draw(Scavenger.AssetManager.TextureMap["game_area"], Vector2.Zero, Color.White);
        spriteBatch.Draw(Scavenger.AssetManager.TextureMap["log_area"], new Vector2(0, Constants.GAME_AREA_HEIGHT), Color.White);
        spriteBatch.Draw(Scavenger.AssetManager.TextureMap["stats_area"], new Vector2(Constants.GAME_AREA_WIDTH, 0), Color.White);
        spriteBatch.Draw(Scavenger.AssetManager.TextureMap["help_info"], new Vector2(Constants.GAME_AREA_WIDTH, Constants.SCREEN_HEIGHT - 52), Color.White);

        DrawStats(spriteBatch);
        TryRedrawLog(spriteBatch);
        WriteLog(spriteBatch);
    }

    private void SetRedrawLogFlag(object sender, EventArgs e)
    {
        redrawLogFlag = true;
    }

    private void TryRedrawLog(SpriteBatch spriteBatch)
    {
        if(redrawLogFlag)
        {
            redrawLogFlag = false;

            logRenderTarget = new RenderTarget2D(
                this.graphicsDevice,
                Constants.GAME_AREA_WIDTH,
                Log.Height
            );

            this.graphicsDevice.SetRenderTarget(logRenderTarget);
            this.graphicsDevice.Clear(Color.Black);

            for (int i = 0; i < Log.Count; i++)
            {
                spriteBatch.DrawString(Scavenger.AssetManager.Font12, 
                    Log.Entries[i], 
                    new Vector2(Constants.LOG_MARGIN, Constants.LOG_MARGIN + i * Scavenger.AssetManager.Font12.LineSpacing), 
                    Color.GreenYellow
                );
            }

            this.graphicsDevice.SetRenderTarget(null);
        }
    }

    private void WriteLog(SpriteBatch spriteBatch)
    {
        spriteBatch.Draw(logRenderTarget,
            new Rectangle(0, Constants.GAME_AREA_HEIGHT, Constants.GAME_AREA_WIDTH, Constants.LOG_HEIGHT),
            new Rectangle(0, 0, Constants.GAME_AREA_WIDTH, Constants.LOG_HEIGHT),
            Color.White
        );
    }

Solution

I decided to switch to using a Viewport. It seems, however, that MonoGame uses the last set-up Viewport before the call to spriteBatch.End(). It also seems that it is the same with the ScissorRectangle, so I could have made it also work. I have added the ScissorRectangle-specific code here in comments. Here's my new class:

public class LogWriter
{
    private GraphicsDevice graphicsDevice;

    private Viewport defaultViewport, logViewport;
    //private Rectangle scissor, scissorBackup;

    public void Init(GraphicsDevice graphicsDevice)
    {
        this.graphicsDevice = graphicsDevice;

        defaultViewport = this.graphicsDevice.Viewport;
        logViewport = new Viewport(0, Constants.GAME_AREA_HEIGHT, Constants.GAME_AREA_WIDTH, Constants.LOG_HEIGHT);

        //scissor = new Rectangle(0, Constants.GAME_AREA_HEIGHT, Constants.GAME_AREA_WIDTH, Constants.LOG_HEIGHT);
        //scissorBackup = this.graphicsDevice.ScissorRectangle;
    }

    public void WriteLog(SpriteBatch spriteBatch)
    {
        this.graphicsDevice.Viewport = logViewport;
        //this.graphicsDevice.ScissorRectangle = scissor;

        spriteBatch.Begin();
        //spriteBatch.Begin(SpriteSortMode.Deferred, null, null, null, new RasterizerState() { ScissorTestEnable = true });

        for (int i = 0; i < Log.Count; i++)
        {
            spriteBatch.DrawString(Scavenger.AssetManager.Font12,
                Log.Entries[i],
                new Vector2(
                    Constants.LOG_MARGIN,
                    Constants.LOG_MARGIN - 100 + i * Scavenger.AssetManager.Font12.LineSpacing),
                Color.GreenYellow
            );
        }

        spriteBatch.End();

        this.graphicsDevice.Viewport = defaultViewport;
        //this.graphicsDevice.ScissorRectangle = scissorBackup;
    }
}

Init() is called in the LoadContent() function. WriteLog() is called in the Draw() function after End() has been called on the spriteBatch after drawing all the other things.