reserve x for set;
reserve a, b, c, d, e for Real;
reserve m, n, m1, m2 for Nat;
reserve k, l for Integer;
reserve p for Rational;

theorem
  a>0 & a<>1 & b>0 implies log(a,b to_power c) = c * log(a,b)
proof
  assume that
A1: a>0 and
A2: a<>1 and
A3: b>0;
A4: b to_power c > 0 by A3,Th34;
 a to_power (c*log(a,b)) = (a to_power log(a,b)) to_power c by A1,Th33
    .= b to_power c by A1,A2,A3,Def3;
  hence thesis by A1,A2,A4,Def3;
end;
