He practiced law in Brownsville. He served as chairman of the board of trustees of Brownsville; as county attorney of Edmonson County 1902–1903; as assistant
Attorney General of Kentucky 1912–1915; as
Attorney General of Kentucky 1915–1917; and as chairman of the Kentucky Tax Commission 1917–1918. He then moved to
Louisville, Kentucky, in 1918 and then to
Bowling Green, Kentucky, in 1922, continuing to practice law. He served as a member of the State Board of Education, the State Board of Sinking Fund Commissioners, and the State Board of Printing Commissioners. He served as a justice of the
Kentucky Court of Appeals 1926–1930 and as
Chief Justice in 1931. Logan was elected as a Democrat to the
United States Senate in
1930, defeating Republican
John M. Robsion, who had been appointed to fill the seat of
Frederic M. Sackett, who had become ambassador to Germany. (Democrat
Ben M. Williamson defeated Robsion for the rest of the unexpired term, which ended March 3, 1931.) He was
re-elected in 1936, narrowly defeating former governor and senator
J.C.W. Beckham in the primary election. He served in the Senate from March 4, 1931, until his death. While in the Senate he served as chairman of the Committee on Mines and Mining (Seventy-third through Seventy-fifth Congresses) and on the Committee on Claims (Seventy-sixth Congress). In 1933 Logan chaired the subcommittee dispatched to
Louisiana by the
United States Senate to investigate allegations of corrupt activities of the political machine of
Huey Long during the 1932 election of
John H. Overton to the Senate. Logan's inquiry reported that the election was impacted by fraud, specifically the involvement of
dummy candidates and deducts (money taken from public employees' pay for use by the Long machine), but no action was taken against Overton. == Personal life ==