Graphical Representation of Logarithm Function

Q. The number of solutions of the equation
$|\ln |x||-||x|-1|=0$ is

Q. The number of solutions of ${\log }_2(x+5)=6-x$ is

Q.

If $a={\pi }^{3e},b=3^{\pi e}andc=e^{3\pi },$ then

1. a<b<c
   

2. b<a<c
   

3. c<a<b
   

4. a<c<b

Q. The number of solution(s) of $e^x=|x|$ is

1. $2$
2. $3$
3. $0$
4. $1$

Q. If $x{\log }_{e}x=a,\text{and}aϵR,$ then match the following

Column I	Column II
(A) Equation has one real root	(p) $a<-\frac{1}{e}$
(B) Equation has 2 different real roots	(q) $a\ge 1$
(C) Equation has 2 equal roots	(r) $a=-\frac{1}{e}$
(D) Equation has no real roots	(s) $-\frac{1}{e}<a<0$
	(t) $a\ge 0$

1. A(q, t), B(s), C(r), D(p)

Q. The number of solutions of ${\log }_3(x-3)=4-x$ is

1. $0$
2. $1$
3. $2$
4. infinite

Q. The number of solutions of ${\log }_2(x+5)=6-x$ is