Suppose . What is ?

81^x = 64   by taking the log of both sides, x = log64 / log 81

So

27^x+1 =  27^{( log64 / log 81  + 1)} = about 610.94

This problem would give a "nice" answer if 64 were a power of 3; however, ...

Problem:         81^x  =  64

Take the log of both sides:                  log(81^x)  =  log(64)

Exponents come out as multipliers:    x·log(81)  =  log(64)

--->                                                           x  =  log(64) / log(81)  ≈  610.940

27^{x + 1}  =  27^{610.940 + 1}  =  27^611.940