From the 1986 British young adult mystery novel, The Three Detectives and the Missing Superstar by Simon Brett.
Blurb from the back of the book:
When Dazzleman, lead singer of the chart topping group Reddimixx, disappears, only Emma Cobbett and her friends think there may be more to it than a publicity stunt. But can the Three Detectives prove that Dazzleman has been kidnapped? And for what?