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Dictionary.com Unabridged (v 1.1) STUDY: 1.application of the mind to the acquisition of knowledge, as by reading, investigation, or reflection:
(under synonyms)
Study implies an attempt to obtain a grasp of something by methodical or exhaustive thought: to study a problem.
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The specific English word meaning "to exert one's self, endeavour, give diligence",
in the context of thought, is
study.
There is no obsolete or ancient meaning used in the definition of "study" as used in this verse. It is ordinary current usage. The KJV translation of this verse is perfectly correct and good ordinary modern English.