3^a + 9^a + 27^a = 39

 = 39
 = 39
 = 39
 = 39 ------ Substituting t for 
 <==== The highest exponent is 3, so there're THREE (3) solutions to this equation.
Using the RATIONAL ROOT theorem, we find that 3 is a ROOT of the equation. Therefore, t = 3, so t - 3 = 0, and t - 3 
is a factor. With 3 being a root, we use SYNTHETIC DIVISION or LONG DIVISION of POLYNOMIALS to find the other factor.

The former gives us:    3 | 1 | 1 |  1 | - 39 |
                          |   | 3 | 12 |   39 |
                          | 1 | 4 | 13 |    0 |

Thus, the other factor is: , and so,  becomes: , which gives us: 
              t - 3 = 0       or      
                  t = 3       or     The DISCRIMINANT for the quadratic is: .
                                     With the DISCRIMINANT being NEGATIVE (< 0), 2 of the roots to this quadratic are 
                                     IMAGINARY/COMPLEX.

            Since t = 3, the ONLY REAL root is 3.

                  t = 3 
                 = 3 ------ Back-substituting  for t
                 
As the BASES are equal, so are the EXPONENTS. As such, a = 1.