Martha Logan was born in Hartford, Connecticut on July 27, 1863. Her mother, the daughter of Mr. and Mrs. William Alexander, was born into an established Toronto family.

In Ontario, Martha Logan was educated at the Toronto School of Art, where she won a gold medal, a silver medal for industrial design and a bronze medal for drawing from life, and the Ontario College of Art. In London, England, she attended the Royal College of Art, where she studied under Lauterni, and the South Kensington School, where she was the first foreign student to be admitted. She also studied at the Buffalo Art League, under Bridgman, and the Ontario School of Art, under Lucius O'Brien.

She painted ceramics, and in oils and water-colours. She began teaching in 1885, and taught art at Winchester Street Public School in Toronto from 1906 to 1928.

In addition to WAAC exhibitions, her work was shown through the Art Association of Montreal (later the Montreal Museum of Fine Arts), the Ontario Society of Artists, and at the Royal Canadian Academy.

She died in Welland, Ontario in 1937. Examples of her work can be found in a Government of Ontario collection.

Martha Logan painted 12 dinner plates for the dinner service.