Current Browsers:

// DOM collection as proper array

const matches = Array.from(document.querySelectorAll('[id^=log_]'));

Older Browsers: (IE9+)

// Use Array.prototype.slice to turn the DOM collection into a proper array

var matches = [].slice.call(document.querySelectorAll('[id^=log_]'));

jQuery:

$('[id^=log_]')

Really Old Browsers, no jQuery:

var matches = [];

var elems = document.getElementsByTagName(*);

for (var i=0; i<elems.length; i++) {

  if (elems[i].id.indexOf(log_) == 0)

    matches.push(elems[i]);

}

//matches now is an array of all matching elements.