Photoshop is the app for creating logos, but you need Illustrator to generate the SVG code. This is a tutorial that focuses on opening your logo in illustrator and exporting your logo.
1. Open Your Logo in Illustrator
Open your logo in Illustrator > select Convert Layers to Objects > click OK.
2. Export Your Logo
File > Export > Export As... > Format: SVG (svg) > click Export.
Decimal: 3 > click Show Code.
Copy and paste code into your website. Done!