A logo is the most important part of any business. Logos are the chief visual component of a company's overall brand identity. It's the first thing people see and come to think of when they think of a business. Any successful business starts with a professionally, well designed logo. Good logos should be unique and comprehensible to potential customers in your target market. It should help convey some information about a company, or even give some sense of meaning about a company or its industry.
When it comes to the tools used to digitally create a logo, there is one that should be used. Adobe Illustrator is by far the best program for the job. Sure, other programs like Adobe's Photoshop that technically can do the job, but not well. Illustrator is called a vector program, which means it uses math to draw shapes using points, lines and curves. Photoshop is a raster program, which uses tiny squares of color information, we call pixels. Here is an example of images in both programs.
A vector program like Illustrator allows for images to be scalable to any size. For instance, if you design a logo at 2 inches by 3 inches with vector objects in Illustrator, it can be scaled up to be put on the side of a skyscraper without losing any resolution. It will not be pixelated or fuzzy. Raster programs can only do a file at the exact size the file should be. If you were to design a logo that needs to be placed on a building, you would have to make your Photoshop document size 100% of the width and height of the size it needs to be on the building. Good luck at creating a large enough Photoshop document on even the most powerful computers, because it will still not be able to handle it.
Next, Illustrator also manages to create a smaller file size, which is easier to handle either when proofing or using for any other purpose. A vector file needs only four points of data to recreate a square versus 300 individual pixels for a raster image. For simple graphics, like geometric shapes or typography, this means a much smaller file size and faster processing speed.
Finally, the edibility is much easier and possible in Illustrator. Unlike popular raster-based formats, such as a jpg or png, vector files are not "flattened." When you open them back up in Illustrator, all of the original shapes exist separately on different layers; this means you can modify individual elements without affecting other objects in the image.
In completion, while there is a place in the logo design industry for programs like Photoshop, vector programs like Illustrator should be the first and foremost of choices. In my opinion, it is the only choice for my logo creations. Then I use it however, and where ever need be.