It's been a very longtime since I "played" with a mac as opposed to using it as an appliance, in my case a word processor. But for the first time in a very longtime I downloaded an app from the app store to my 2010 bmp and where it went I have absolutely no idea. I've checked I believe every possible place and nada. any help most appreciated
Welcome back to the Mac sphere.
It should have installed in the Applications section of your Mac. In Finder you should be able to see a folder called "Applications". See if you find it within.
Also try using Launchpad (Gray, circular icon with a rocket ship on it) which is either on your Dock or in Applications folder. Gives you an iOS style launcher for your applications. You can also immediately start typing in this view to narrow down applications. Try typing the name of the application you download.
Alternatively you can also use Spotlight. Click the spyglass in your menu bar in the upper, right region of your screen and type the name of the application to see if you can find it on your Mac.
If all else fails go back to the Mac App Store, click on Purchases and verify that the application has finished downloading to your Mac.