checkPositive("x", x);
    if (fitsInLong(x)) {
      return LongMath.log10(x.longValue(), mode);
    }

    int approxLog10 = (int) (log2(x, FLOOR) * LN_2 / LN_10);
    BigInteger approxPow = BigInteger.TEN.pow(approxLog10);
    int approxCmp = approxPow.compareTo(x);

    /*
     * We adjust approxLog10 and approxPow until they're equal to floor(log10(x)) and