You can use convert's "-verbose" option to see what is happening:
convert -verbose -density 300x300 -resize 800x600 -quality 85 logo: logo: ZIEL.jpg
LOGO GIF 640x480 640x480+0+0 8-bit sRGB 256c 28.6KB 0.020u 0:00.019
logo:=>LOGO GIF 640x480 640x480+0+0 8-bit sRGB 256c 28.6KB 0.000u 0:00.000
LOGO GIF 640x480 640x480+0+0 8-bit sRGB 256c 28.6KB 0.020u 0:00.029
logo:=>LOGO GIF 640x480 640x480+0+0 8-bit sRGB 256c 28.6KB 0.000u 0:00.000
logo:=>ZIEL-0.jpg[0] GIF 640x480=>800x600 800x600+0+0 8-bit sRGB 42KB 0.340u 0:00.330
logo:=>ZIEL-1.jpg[1] GIF 640x480=>800x600 800x600+0+0 8-bit sRGB 42KB 0.210u 0:00.210
Because JPEG is a single-image format, the output is in separate images ZIEL-0.jpg, ZIEL-1.jpg, etc.