To create a log entry in WHMCS there's the LogActivity API ( https://developers.whmcs.com/api-reference/logactivity/ ), with following syntax:

$command = 'LogActivity';
$postData = array(
    'description' => 'Activity log entry text goes here',
);

$results = localAPI($command, $postData;
print_r($results);

But there's also a shorter and faster way to do it:

$description' = 'Activity log entry text goes here';
$results = logActivity($description, 0);
print_r($results);

Or even shorter:

$results = logActivity('Activity log entry text goes here', 0);
print_r($results);

Surprisingly, this function exists but is not documented anywhere.