What will be the outcome of putting litmus paper into a mixture of equal amounts of soap and tomato juice?

There are different types of litmus papers; red, blue, and purple are the most common. Most likely the mixture between soap and tomato juice will have a neutral pH or close to neutral, therefore the color indicated by litmus paper should indicate that of a neutral solution which for those mentioned wouldn't be too clear. The best option will be using a universal indicator instead which will show a green color when neutral. Red litmus paper turns blue when placed in a basic solution. Blue litmus paper turns red in an acidic solution, but none of them will show a clear color when placed in a neutral solution.