Despite the warning, your problem should have been solved using Mosek’s native exponential cone capability. That the warning was issued is a known "bug’, and can be ignored. The warning message was created when the successive approximation method was the only solution method for problems in the log and exp family. But it is still issued, even though there are now other solution methods which may be invoked (native exponential cone or CVXQUAD’s Padé approximant).
If you don’t use the quiet option, you will see the solver output log.