reserve D for non empty set,
  i,j,k,l for Nat,
  n for Nat,
  x for set,
  a,b,c,r,r1,r2 for Real,
  p,q for FinSequence of REAL,
  MR,MR1 for Matrix of REAL;

theorem Th5:
  a>0 & a<>1 & b>0 implies -log(a,b) = log(a,1/b)
proof
  assume that
A1: a>0 and
A2: a<>1 and
A3: b>0;
  thus -log(a,b) = 0 - log(a,b) .= log(a,1) - log(a,b) by A1,A2,POWER:51
    .= log(a,1/b) by A1,A2,A3,POWER:54;
end;
