"Their relationship was based on mutual respect"
Why do we always use "base on" in passive? Can we use it not in the passive?
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You can actually use "base on" in the active voice. It means
To ground (an opinion, a conclusion, etc.) on — i.e. to give reasons for something
To derive (a work) from — i.e. to adapt something
Note that in the active voice, the object comes between "base" and "on". Here are two examples:
They decided to base their relationship on mutual respect.
John Milton based his masterpiece "Paradise Lost" on ancient epic poems.
One particular construction in which you must use the passive voice is this:
Based on our previous results, we decided that a follow-up study was necessary.
Here, "based on" is a fixed expression that means something like "in light of" or "given".
The preposition on in your example has nothing to do with the type of voice a verb is in. Rather, the preposition to be used after a verb has to do with the prepositional valency required by that verb.
For the verb
to base [something] on [something], the preposition to be used after it, which which it forms a unit of sense often distinct from that of the verb when taken on its own, is always on.
You aren't right that "base " is always used in the passive voice. You can write your sentence in a different way :
1) They based their relationship on mutual respect. (It's an active use)
I am giving you some more examples to completely understand.
2) ‘I've read poor reviews here, and elsewhere, about the conductor, so I base my conclusions on that…!’
3) ‘Dershwitz based his conclusion on witnesses who said Reid had slurred speech and difficulty holding up his head at the start of the interview.’
4) ‘Although he based his films on Kannada novels, the novelists complained that their stories had been altered.’
Hope it helps you out.