Logarithmic Inequalities

Q.

Solution set of the inequality $lo{g}_{0.8}\left(lo{g}_6\frac{x^2+x}{x+4}\right)<0$

1. (-4, -3)

2. $(-3,4)\cup (8,\infty )$
   

3. $(-4,-3)\cup (8,\infty )$

4. $(-3,\infty )$
   

Q. $lo{g}_{(x-2)}(2x-3)>lo{g}_{(x-2)}(24-6x)$
The solution set of the above inequality has integral values of x ___

Q. If $lo{g}_{0.04}(x-1)\ge lo{g}_{0.2}(x-1)$ then x belongs to the interval

1. $Noneofthese$
2. $(1,2]$
3. $(-\infty ,2)$
4. $[2,+\infty ]$

Q. If A is the set of all $xϵR$ such that $x^{(logx{)}^2-3logx+1}>1000$, and $A=(a,\infty )$ then $\sqrt{10a}$ will be ___

Q. The set of real values of x for which $2^{{log}_{\sqrt{2}}(x-1)}>x+5$ is

1. $Noneofthese$
2. $(-\infty ,-1)\cup (4,+\infty )$
3. $(4,+\infty )$
4. $(-1,4)$

Q. If $lo{g}_{03}(x-1)<lo{g}_{009}(x-1)$, then x lies in the interval

1. $(-2,-1)$
2. $(1,2)$
3. None
4. $(2,\infty )$

Q.

If $lo{g}_{0.5}(x-1)<lo{g}_{0.25}(x-1),$ then x lies in the interval.

1. $(2,\infty )$

2. $(3,\infty )$

3. $(-\infty ,0)$

4. (0, 3)

Q. If $x=lo{g}_5\left(1000\right)$ and $y=lo{g}_7\left(2058\right)$ then

1. x < y
2. x = y
3. None of these
4. x > y

Q. The number $lo{g}_{20}$ 3 lies in

1. $(\frac{1}{4},\frac{1}{3})$
2. $(\frac{1}{3},\frac{1}{2})$
3. $(\frac{1}{2},\frac{3}{4})$
4. $(\frac{3}{4},\frac{4}{5})$

Q.

If $x\in R$ satisfies $(lo{g}_{10}100x{)}^2+(lo{g}_{10}10x{)}^2+lo{g}_{10}x\le 14$ then $x$ contains the interval

1. (0, 10)

2. $[{10}^{\frac{-9}{2}},10]$
   

3. $(0,\infty )$
   

4. $(-1,\infty )$