Question

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

विकल्प

• x – 1 > y

• x² + 1 > y

• y > x – 1

• ${\displaystyle \frac{x+1}{x<y}}$

Answer 1

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

Explanation:

f'(x) = x – 1 – log x

f'(x) = ${\displaystyle 1-\frac{1}{x}}$

= ${\displaystyle \frac{x-1}{x}}$

f(x) ↑ in [1, ∞)

f(x) > 0 for [1, ∞)