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answers:
david say: y = lnx
dy = (1/x) dx
dx = 3 - e
dy = (1/e)(3 - e) = (3/e) - 1
since ln e = 1. y = 1 + (3/e) - 1 = 3/e <<<< answer
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rotchm say: f(x) ≈ f(a) + f '(a)(x-a)

Here, a = e . Then x = 3.
Plug these in, dp the simplification correctly, and your answer is there.
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Ash say: f(a) ≈ f(b)+f′(b)(a-b)
f(a) = ln3
f(b) = y = lnx = lne
f'(b) = 1/x = 1/e

f(a) ≈ f(b)+f′(b)(a-b)
ln3 ≈ lne + (1/e)(3-e)
ln3 ≈ 1 + (3-e)/e
ln3 ≈ (e + 3 - e)/e
ln3 ≈ 3/e
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