Why do creationists believe the world was created 6k years ago?

Not true. The day-night cycle is established at the start of day one (Genesis 1:3-5). There is nothing stating nor implying that the day length is anything different from the current 24 hours.And of course, scientifically, the length of day is determined by the rotation of the Earth - not the sun or the moon.

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The Bible does not designate the length of the days before day 5 after the sun and moon were created.

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It doesn't designate the length of time for days 5, 6 or 7 either. But you have no problem assuming that they are 24 hours. Where does it say that the length of the days changed ? Where does it say that the lengths of days 1 to 4 was anything other than 24 hours ? Where does it say that the length of days 1-4 were any different from days 5-7 ?Nowhere.

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The sun & moon likely have a bearing on the rotation of the earth as well as the 24 hour day.

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No, it's not likely. Not in the Genesis account where day and night come before the sun and the moon and where there are mornings and evenings - and plants growing - before the sun and the moon and the stars are created. (Do you really think that plants would thrive in a million years of more of darkness ?)

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Also the text specifically says that the sun & moon were to determine the days and seasons etc.

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Which refers to measurements, not changing the time periods involved.

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I go with the Bible but when the science applies imo it should be applied.

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Neither suggests that the length of day changed (or would change) in the Genesis 1 creation account.