Logarithmic inequalities

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 $\frac{1}{{\log }_3\mathrm{\pi }}+\frac{1}{{\log }_4\mathrm{\pi }}>x$, then $x$ will be

1. $3$

2. $2$

3. $4$

4. None of these

Q.

The conjugate of $\frac{1}{\left(3+4i\right)}$ is

Q.

The set of all $x$satisfying the inequality$\frac{4x-1}{3x+1}\ge 1$ is

1. $(-\infty ,–\frac{1}{3})\cup (\frac{1}{4},\infty )$

2. $(-\infty ,–\frac{2}{3})\cup (\frac{5}{4},\infty )$

3. $(-\infty ,–\frac{1}{3})\cup [2,\infty )$

4. $(-\infty ,–\frac{2}{3})\cup [4,\infty )$

5. $(-\infty ,–\frac{1}{3})\cup (\frac{1}{2},\infty )$

Q.

Solve: ${\log }_{0.2}$ |x-3| $\ge$ 0

1. x ∈ [2, 4]

2. x ∈ [2, 4] - {3}

3. x ∈ [-2, 4]

4. x ∈ [-2, 4] -{3}

Q.

find x if ${\log }_2(x-5)>3$

1. x>5

2. x>13

3. x<13

4. x>8

Q.

Prove that $7\log \left(\frac{16}{15}\right)+5\log \left(\frac{25}{24}\right)+3\log \left(\frac{81}{80}\right)=\log 2$

Q.

The solution set of the inequality
$\sqrt{6-x}(5^{x^2-7.2x+3.9}-25\sqrt{2})\ge 0$ can be given by $(-a,\frac{b}{c})$, then c - b = ___

Q.

Solve for $x$:

$lo{g}_3\left(\frac{x}{3}\right)+lo{g}_{1/9}\left(x\right)<1$

1. (0, 81)

2. $(-\infty ,1)$

3. $(-\infty ,-2)\cup (-2,-1)\cup (-1,0)$

4. None of these.

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

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

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. If $lo{g}_{\frac{1}{\sqrt{2}}}(x-1)>2$ then x lies in the interval

1. $(\frac{3}{2},\infty )$
2. $(-\infty ,\frac{3}{2})$
3. $(\frac{3}{2},1)$
4. None of these

Q. The set of real values of x for which $lo{g}_{0.2}\frac{x+2}{x}\le 1$ is

1. $(-\infty ,-\frac{5}{2}]\cup (0,+\infty )$
2. $[\frac{5}{2},+\infty )$
3. $(-\infty ,-2)\cup (0,+\infty )$
4. $Noneofthese$

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

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

Q. If ${\log }_{0.5}\frac{3-x}{x+2}<0$, then the number of integral values of x is

1. 3
2. 4
3. 2
4. 1

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. x = y
4. None of these

Q. If $x=lo{g}_{5}3+lo{g}_{7}5+lo{g}_{9}7$, then x $\ge$

1. $\frac{1}{2^{\frac{1}{3}}}$
2. $\frac{3}{2^{\frac{1}{3}}}$
3. None
4. $\frac{3}{2}$

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. The least value of $2lo{g}_{100}a-lo{g}_a\left(0.0001\right),a>1$ is

1. 2
2. 3
3. None
4. 4

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. $(-3,\infty )$
   

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

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)