I am assuming you have placed the image into the header area of the Survey Settings > Headers and Footers section of your survey so that the logo appears on all of the pages of the survey. To remove it on the start page, you can just need a little custom HTML and CSS. Essentially you will place the image into a div with an ID, and then use some CSS on the start page to hide that div. Below is some sample code:
<img src="image.jpg" alt="" border="0">
Then place this code on your start page, such as in the footer of that question.