P.S. - I am having the same issue with both SQL 2012 and 2014 LocalDB.
I have been looking for days for the answer to this question, and have installed, uninstalled, repaired, etc. I have deleted, and created instances, I have corrected Environment Path, moving the SQL 2014 paths to the beginning of the path.
I have VS2013 installed.
I have SQL 2014 SQL Express with tools and LocalDB installed.
I have VS2013 configured as follows:
TOOLS -> Options -> Database Tools -> Data Connections -> (LocalDB)\ProjectsV12
"SQLLocalDb info" showed that ProjectsV12 exists, but "SQLLocalDb start ProjectsV12" failed to start, so I deleted it and recreated and started it with the following commands:
"SQLLocalDb delete ProjectsV12"
"SQLLocalDb create ProjectsV12"
"SQLLocalDb start ProjectsV12"
LocalDb starts just fine, no errors in error.log either.
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