What is a base used in toothpaste sorbitol carrageenan magnesium hydroxide sodium lauryl sulfate

Answer is "magnesium hydroxide".

Among the given choices, magnesium hydroxide is the base. Normally toothpastes are alkali or neutral.

Mild base is used to neutralize the acids which are produced by bacterial activities.

The pH of the toothpastes is a very important factor. Low pH values which are below 5.5 are not good for your enamel.