Preheat the oven to 350°F (175°C). Grease a 9-inch cake pan.
In a mixing bowl, whisk together the flour, baking powder, and salt.
In another bowl, combine the yogurt, sugar, eggs, and lemon zest. Mix well.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Fold in the vegetable oil until the batter is smooth.
Pour the batter into the prepared cake pan and bake for 45 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.