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Yes, egg size can make a large difference. Especially for trickier recipes or for larger sized items, and especially when doubling a recipe. For some simple stuff, there is lots of room for leeway so you won't notice. To be safe, use a large egg. Most recipes are designed for large eggs. More precise recipes will use weight, but home cooks can also rely on volume. Use between 3 Tbsp and a scant quarter cut of lightly beaten egg for each egg called for. Here is a good resource:
Baking recipes call for large eggs unless otherwise specified. It is supposed to matter, but remember that measuring cups and spoons are wildly inaccurate, so unless your recipe has a lot of eggs it probably doesn't.
Most recipes call for large - and, at room temp.
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