Historically, the Logopolitans only used machines for simple tasks and very rarely had any need for technology; every Logopolitan worked on their section of an equation with an abacus. (TV: Logopolis) They were the first to develop Block Transfer Computations. (PROSE: Cat's Cradle: Witch Mark)
At some point before the 20th century, the Logopolitans discovered that the universe had already reached its point of collapse due to the advance of entropy. To maintain its existence, they built CVEs, which opened up the universe, N-Space, into a smaller one, E-Space, moving the entropy into the other universe. The Logopolitans, through their Block Transfer Computations, copied the Pharos Project on Earth and used it to relay computations to the CVEs. This preserved the universe while they sought a more permanent solution.
In 1981, the Master arrived on Logopolis and killed several Logopolitans. As a result the structure of the planet unravelled and Logopolis was silenced forever. The constant calculations for the CVEs were stopped and entropy built up, killing the entire Logopolitan race as well as many other planets and races. (TV: Logopolis)