How would i solve the problem:
e^4x=120

 x =  1.1968729357 ;  or, round to: 1.2 .
 You would take the "ln" (that is, "natural logarithm") of EACH side of the equation:

ln (e^4x) = ln (120); 

Then continue:

4x  ln e = ln 120

4x = ln 120 ;  (since "ln e = 1")

then divide EACH side of the equation by "4", to isolate "x" on one side of the equation; and to solve for "x" ;

  4x / 4 = (ln 120) / 4 ;

 x = (ln 120) / 4 ; 

 Using a calculator:

  x = (ln 120) / 4 = (4.78749174278) / 4 =  1.1968729357
 x =  1.1968729357 ;  or, round to: 1.2 .