Changing the scale of an extent for a layout using PyQGIS

I have a script that creates a print layout and contains all of my vector/raster layers. I have changed my extent to ‘mem_layer’, which is my buffer layer I am using for this project. However, when I view the print layout, the extent is so far zoomed in on the buffer layer, that it is impossible to view the location around it. If I go into the layout manually and change the scale to 8500000, then my map works perfectly. Using PyQGIS, is there any way I can incorporate to add/change the scale of the extent to 8500000, so that I can view my map more clearer. My script is as follows:

project = QgsProject.instance()             #gets a reference to the project instance
manager = project.layoutManager()           #gets a reference to the layout manager
layout = QgsPrintLayout(project)            #makes a new print layout object, takes a QgsProject as argument
layoutName = "PrintLayout"

layouts_list = manager.printLayouts()
for layout in layouts_list:
    if layout.name() == layoutName:
        manager.removeLayout(layout)
        
layout = QgsPrintLayout(project)
layout.initializeDefaults()                 #create default map canvas
layout.setName(layoutName)
manager.addLayout(layout)

#This adds a map item to the Print Layout
map = QgsLayoutItemMap(layout)
map.setRect(20, 20, 20, 20)  
#Set Extent
#rectangle = QgsRectangle(1355502, -46398, 1734534, 137094)         #an example of how to set map extent with coordinates
#map.setExtent(rectangle)
canvas = iface.mapCanvas()
map.setExtent(mem_layer.extent()) 
layout.addLayoutItem(map)
#Move & Resize
map.attemptMove(QgsLayoutPoint(5, 27, QgsUnitTypes.LayoutMillimeters))
map.attemptResize(QgsLayoutSize(239, 178, QgsUnitTypes.LayoutMillimeters))

What the map on the layout currently shows:

What I would like the map to show when I change the scale is 8500000 using PyQGIS:

# [...]
map.setExtent(mem_layer.extent())
map.setScale(8500000)
# [...]