Website Logo - Image Type File Formats

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I am new to web design and I am currently developing a website now, Al-Joufi Law Firm | Law Firm in Saudi Arabia, Saudi Lawyers and Legal Advisors, Commercial, Companies and Business Law in Saudi. What is the best image file format that I could use for the website logo that renders high resolution even zoomed in. I appreciate it if you could please take a look at the logo and let me know your thoughts on it.

The current logo of the website that i am doing now, seems to be blurry and pixelated when you zoom it in. This is PNG format.

I really appreciate your help and suggestions how i could do this properly.
I know this is an old thread but it may be of help to someone else. What you need to create is a vector image. Vector images have no fixed resolution, which means they can be increased to any dimension without loosing the image quality. They are great for print ads, flash animations, logos etc. Once you have created a vector image you can then export it in png or jpeg format. I use Inkscape which is a free vector image creator