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Preheat oven to 425 Grease a 9x13 inch pan and line with parchment paper.
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Sift together flour, baking powder, and salt into a small bowl. Set aside.
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Beat eggs and sugar together on high speed until pale and thick. Beaters should leave a trail when taken out of the mixture.
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Gently fold the flour into the egg mixture.
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Divide batter into six small bowls and add desired amount of one food coloring to each bowl. Stir to mix in the food coloring and place each colored batter in a separate piping bag.
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Starting with red, pipe each color of batter into the prepared pan to make a rainbow pattern. Pipe along the short side of the pan, repeating until the pan is full.
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Bake for 6-7 minutes or until the cake shrinks away from the sides of the pan.
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While the cake is baking, lay a piece of parchment paper sprinkled with powdered sugar on a flat work surface.
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Once cake is baked, invert the cake onto the prepared parchment paper.
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Remove the parchment paper liner that the cake was baked in and replace with a fresh piece of parchment paper.
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Carefully roll the cake, starting with the short end and place, rolled, on a wire rack to cool.