Who invented the logo programming language?

That depends entirely on which definitions of "invent" and "programming language" you are using!

Countess Augusta Ada King (commonly known as Ada Lovelace), was history's first computer programmer. She took a great interest in Charles Babbage's design idea for a computer (which he called the Analytical Engine), and in 1843 she wrote a computer program to calculate Bernoulli Numbers, designed to run on Babbage's Engine. Although the Engine was never produced in either of their lifetimes, Lovelace's example program is preserved in her notes and, had Babbage finished the Engine, it would have executed perfectly. Therefore, Ada Lovelace was the first to find a method with which to write instructions that could be comprehended and executed by a computer. This is a common dictionary definition of a programming language, but it's not quite the same as a modern programming language.

During the 1940's, Konrad Zuse created the first working, program-controlled computer. Programs were read off punched tape. Zuse also designed the first high-level programming language, Plankalkül, but there was little interest in his papers and it wasn't implemented until the 1970's, decades after many other modern programming languages had been created.

After the computer was created, programmers used assembly language to write their instructions, but assembly is essentially machine code (binary) in a more human-readable format. Each computer had its own version of assembly, and most were built as part of a collaborative process within a company.

In 1953, John Backus proposed FORTRAN to his bosses at IBM. FORTRAN was the first modern programming language to be created and implemented; it was followed shortly by COBOL and LISP. FORTRAN might not be as fancy as some of the languages we have today, but it definitely has a lot in common with them. It included if statements, loops, basic mathematical operators, and file input/output. Later versions introduced data types, subroutines, and comments, to name a few.