reserve x,y,a,b,c,p,q for Real;
reserve m,n for Element of NAT;

theorem
  for a,x being Real st a>0 & a<>1 & a to_power x = a holds x=1
proof
  let a,x be Real;
  assume that
A1: a>0 & a<>1 and
A2: a to_power x = a;
  x=log(a,a) by A1,A2,POWER:def 3;
  hence thesis by A1,POWER:52;
end;
