Should be fine now.
I've edited your tpls/blocks/off-canvas.php file and added a condition which checks if the user is logged in and display different text depends on this condition:
<button class="btn btn-default off-canvas-toggle <?php $this->_c('off-canvas') ?>" type="button" data-pos="<?php echo $this->params->get('off-canvas-position'); ?>" data-nav="#t3-off-canvas" data-effect="<?php echo $this->getParam('addon_offcanvas_effect', 'off-canvas-effect-4') ?>">
<i class="fa fa-bars"> <?php
if ($user->id != 0) {
echo 'Log out';
} else {
echo $this->getParam('off-canvas-trigger-text');
}
?>
</i>
</button>
before that I've defined variables:
$user = JFactory::getUser(); // Get the user object
$app = JFactory::getApplication(); // Get the application
Cheers
Joshua