appeal against
To attempt to change a legal decision. Don't worry, we will appeal against the judge's sentence.
appeal to
1. To ask for something, usually in an urgent or pleading manner Appeal to your congressmen if you really want lower taxes.
2. To spark one's interest or appreciation. Tall, dark-haired guys always appeal to me. That style of architecture just doesn't appeal to me.
3. To resonate with one's specific interests or feelings. The beauty of her prose appeals to my poetic sensibilities. The idea of stronger laws for criminals appeals to me as a mother.