solve this task - http://d2dm5kfavr4eqq.cloudfront.net/tasks/01/task.png

task_6.html

<script src="//code.jquery.com/jquery-2.1.0.min.js"></script>

Result: <div id="result"></div>

<script>
  function hasAllPatterns(string) {
    
    var requiredDigits = [
        0,
        1,2,3,4,5,6,7,8,9,
        'a', 'b', 'c', 'd', 'e'
    ];
    
    for (var i=0; i< requiredDigits.length; i++) {
        if (string.indexOf(requiredDigits[i]) == -1) {
            return false;
        }
    }
    
    return true;
}

var num = 2,
    multiplier = 0,
    stop = false,
    res = 0,
    strNum,
    base = 15,
    $result = $('#result')
;

while (!stop) { 
    res = Math.pow(num, multiplier)
    strNum = res.toString(base);
    $result.html(strNum);
    if (hasAllPatterns(strNum)) {
        stop = true;
        $result.append('<br>Multiplier: '+multiplier);
        return;
    }
    multiplier++;
}
</script>