The expression is think positive. It likely developed from think in a positive way or something similar and got shortened. Otherwise you are right, it should be think positively.
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AnonymousAnother commonly misused word is "fast". It is often used this way: " I sometimes drive too fast." It should be: "I sometimes drive too quickly."Sorry, but this is nonsense. "fast" is a perfectly good adverb. (There is no "fastly".)