1. Tardigrade
  2. Question
  3. Mathematics
  4. If log 0.04(x-1) ≥ log 0.2(x-1), then x belongs to the interval

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

Continuity and Differentiability

Solution:

image
$ \frac{1}{2} \log _{0.2}(x-1) \geq \log _{0.2}(x-1) $
$x-1>0 \Rightarrow x>1$
$\sqrt{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 $
$x \in[2, \infty)$