reserve x,y,t for Real;

theorem Th29:
  x<>0 implies exp_R(x)<>1
proof
  assume
A1: x<>0;
  assume
A2: exp_R(x)=1;
  x=log(number_e,exp_R(x)) by TAYLOR_1:12
    .=0 by A2,Lm1,POWER:51,TAYLOR_1:11;
  hence contradiction by A1;
end;
