The interval in which y= ln ( ln (x)), x1 is decreasing is

Question

The interval in which y= ln ( ln (x)), x>1 is decreasing is (A) (-∞, 0) ∪(2, ∞) (B) (0,2) (C) (0,1) (D) (-1,0)

Tardigrade Admin · Accepted Answer

Given function y=l( ln (x)), x>1 ∴ (d y/d x)=(1/x ln x), x>1 ∵ y is a decreasing, then ∵ x>1 ⇒ ln x<0 ⇒ x<1, which is not possible as x>1 ∴ x ∈ varphi, for decreasing

Q. The interval in which $y = ln (ln (x)), x > 1$ is decreasing is

$(- \infty, 0) \cup (2, \infty)$

$(0, 2)$

$(0, 1)$

$(- 1, 0)$

None of the above

Given function $y = l (ln (x)), x > 1$
$∴ \frac{d y}{d x} = \frac{1}{x l n x}, x > 1$
$∵ y$ is a decreasing, then
$∵ x > 1 \Rightarrow ln x < 0$
$\Rightarrow x < 1$ , which is not possible as $x > 1$
$∴ x \in φ$ , for decreasing

Q. The interval in which y=ln(ln(x)),x>1 is decreasing is

(−∞,0)∪(2,∞)

(0,2)

(0,1)

(−1,0)