jQuery Simple Example

HTML

<script src="//www.addressfinder.co.nz/assets/v2/widget.js"></script>
<form>
    <select id='meu_select'>
        <option value='1'>Valor 1</option>
        <option value='2'>Valor 2</option>
    </select>
    <a id="various3" class="various3" href="/relatorio_gastos_rec.php?param">
        <img src="https://cdn2.iconfinder.com/data/icons/windows-8-metro-style/512/edit.png" width="20" height="20" alt="Alterar" /></a>
</form>
<somente_para_visualizar></somente_para_visualizar>

JavaScript

$('#meu_select').change(function() {
    $('#various3').attr('href', '/relatorio_gastos_rec.php?param=' + this.value);
});