Question

y = log x satisfies for x > 1, the inequality ______.

Options

• x – 1 > y

• x² + 1 > y

• y > x – 1

• `(x + 1)/(x < y)`

Answer 1

y = log x satisfies for x > 1, the inequality x – 1 > y.

Explanation:

f'(x) = x – 1 – log x

f'(x) = `1 - 1/x`

= `(x - 1)/x`

f(x) ↑ in [1, ∞)

f(x) > 0 for [1, ∞)