Why is it when I use google chrome and want to go back to the search bar there is no back button on google chrome and I have to go right back to the desk top and click on google chrome again yet in google itself I just click on the back arrow and return to the search bar
It doesn't seem that you have the homepage icon showing on the toolbar. When you shut down Chrome and re-open it then you re-open at the home page which in your case looks as if it is Google search. Clicking on the home page icon would take you back to it. To add the icon click on the 3 barred icon on the far right, choose then under appearance make sure that "Show home button" is ticked.
You can of course type your search in the address bar as Ian in Northampton states.
I fail to understand why your back button cannot be seen. Should be top left.
Ah - I wonder if you click on a search and it opens in a new tab or new window then the forward and back are not highlighted simply because there isn't anything to go back to. However the previous tabs/windows should still be present.
The back button is not in Google it can only be in Chrome.