text{If } log _{0.2}(x-1) log _{0.04}(x+5), | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) We have,$\log _{0.2}(x-1) > \log _{0.04}(x+5)$ $\Rightarrow \log _{0.2}(x-1) > \log _{0.2^{2}}(x+5)$ $\Rightarrow \log _{0.2}(x-1) > \frac{1}{2} \

Vedclass · Accepted Answer

$1 < x < 4$

Vedclass · Answer

(C) We have,$\log _{0.2}(x-1) > \log _{0.04}(x+5)$ $\Rightarrow \log _{0.2}(x-1) > \log _{0.2^{2}}(x+5)$ $\Rightarrow \log _{0.2}(x-1) > \frac{1}{2} \log _{0.2}(x+5)$ $\Rightarrow 2 \log _{0.2}(x-1) > \log _{0.2}(x+5)$ $\Rightarrow \log _{0.2}(x-1)^{2} > \log _{0.2}(x+5)$ $\Rightarrow (x-1)^{2} $[\because \log _{a} x > \log _{a} y \Rightarrow x $\Rightarrow x^{2}-2x+1 $\Rightarrow x^{2}-3x-4 $\Rightarrow (x-4)(x+1) $\Rightarrow x \in (-1, 4)$ Also,for the logarithm to be defined,$x-1 > 0 \Rightarrow x > 1$ and $x+5 > 0 \Rightarrow x > -5$. Combining $x \in (-1, 4)$ and $x > 1$,we get $x \in (1, 4)$.

$\text{If } \log _{0.2}(x-1) > \log _{0.04}(x+5), \text{ then }$

Similar Questions

If $y = 2^{1/\log_x 4}$,then $x$ is equal to

If ${a^x} = bc$,${b^y} = ca$,and ${c^z} = ab$,then the value of $xyz$ is equal to:

If $\log_{4}5 = a$ and $\log_{5}6 = b$,then $\log_{3}2$ is equal to

If $a, b, c \neq 0$ and belong to the set $\{1, 2, 3, \ldots, 9\}$,then $\log _{10}\left(\frac{a+10 b+10^2 c}{10^{-4} a+10^{-3} b+10^{-2} c}\right)$ is equal to

If $\log _k x \cdot \log _5 k = \log _x 5$,where $k \ne 1$ and $k > 0$,then $x$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module