You may use the following code:

dd($your_query->toSql());

Then access the page and your code will halt execution and dump the query as SQL syntax.

By the way, for this exact query you exemplified, the following code works:

DB::table('product')
	->join('price', 'product.productid', '=', 'price.productid')
	->leftJoin('purchaseitem', 'product.productid', '=', 'purchaseitem.productid')
	->where('product.name', '=', 'Superior King Room')
	->whereNotBetween('purchaseitem.datestart', array('2014-01-06', '2014-01-07'))
	->groupBy('product.productid')
	->having(DB::raw('count(`purchaseitem`.`productid`)'), '<', 'product.quantity')
	->take(30);