If log 0.04(x-1) ≥ log 0.2(x-1), then x belongs to the interval

Question

If log 0.04(x-1) ≥ log 0.2(x-1), then x belongs to the interval (A) (1,2] (B) (-∞, 2] (C) [2, ∞) (D) (0, ∞)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/40f927928d9931f240c2e36b62769ee9-.png" /> (1/2) log 0.2(x-1) ≥ log 0.2(x-1) x-1>0 ⇒ x>1 √x-1 ≤ x-1 x2+1-2 x ≥ x-1 x2-3 x+2 ≥ 0 (x-2)(x-1) ≥ 0 x ≤ 1 x ≥ 2 ∩ x>1 x ≥ 2 x ∈[2, ∞)

Q. If $lo g_{0.04} (x - 1) \geq lo g_{0.2} (x - 1)$ , then $x$ belongs to the interval

$(1, 2]$

$(- \infty, 2]$

$[2, \infty)$

$(0, \infty)$

$\frac{1}{2} lo g_{0.2} (x - 1) \geq lo g_{0.2} (x - 1)$
$x - 1 > 0 \Rightarrow x > 1$
$x - 1 \leq x - 1$
$x^{2} + 1 - 2 x \geq x - 1$
$x^{2} - 3 x + 2 \geq 0$
$(x - 2) (x - 1) \geq 0$
$x \leq 1& x \geq 2 \cap x > 1$
$x \geq 2$
$x \in [2, \infty)$

Q. If log0.04​(x−1)≥log0.2​(x−1), then x belongs to the interval

(1,2]

(−∞,2]

[2,∞)

(0,∞)