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 = 1 holds x=0
proof
  let a,x be Real;
  assume that
A1: a>0 & a<>1 and
A2: a to_power x = 1;
  x=log(a,1) by A1,A2,POWER:def 3;
  hence thesis by A1,POWER:51;
end;
