In what ways can PHP developers separate the presentation and logic layers when working with JavaScript to manipulate div elements?

To separate the presentation and logic layers when working with JavaScript to manipulate div elements, PHP developers can use a combination of PHP to generate the necessary HTML structure and JavaScript to handle the dynamic behavior. By embedding JavaScript functions within the HTML elements or linking external JavaScript files, developers can keep the logic separate from the presentation, making the code more maintainable and scalable.

```php
<?php
// PHP code to generate HTML structure
echo '<div id="myDiv">This is a div element</div>';

// JavaScript code to manipulate the div element
echo '<script>
document.getElementById("myDiv").style.color = "red";
</script>';
?>