Quickest 7h 25min
There are 4 buses 3 flights1 train company operating 2 routes - California Zephyr, Texas Eagle from Logan to Austin. The cheapest train costs $404 and is 2d 2h 50min.
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There are 4 ways to travel from Logan to Austin. 4 buses, 3 flights, 3 trains and 1 by car are possible between the two areas. The by car from Logan to Austin is the cheapest. The flight from PVU to AUS is the fastest. The train operated by Amtrak running from SLC to AUS is the most convenient.
It's important to check each mode when booking your ticket so that you can find the best method for you. The cost of each type varies differently, so be sure to use Faretrotter to keep an eye out!