Different homepage for logged in users (redirect to different URL)

1 – User is logged in
2 – Logged in user visits https://www.mywebsite.com (when he clicks on the logo, this is the default static homepage of the website)
3 – Logged in user is redirected to https://www.mywebsite.com/home. This is a different homepage. The static homepage (www.mywebsite.com) contains content which is only meant to be seen by logged out users / non-members.

Also:

– Some pages (besides the homepage) are meant for logged out users only. A logged in users sees a different page.

What I am basically looking for is this:

Logged in user visits URL X, is redirected to URL Y

(Visits test.com, redirects to test.com/1 – visits test.com/new, redirects to test.com/old, etc.).

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Something like this already exists for logged out users. If a logged out users visits a page which is meant for members only, he’s redirected to a different page.

Is this possible?