the symbols used in the story are:

1. house and shops- it symbolizes Aksionov's family and material possessions
2. nightmare-it symbolizes a bad omen.
3. blood-stained knife- it indicates Aksionov's lack of control over his fate.
4. the prison- Aksionov's pain and subsequent mystical transformation are symbolized by the prison.
5. the book(the lives of the saints)- gives an impression of religiosity.

Log_2aa=x    then, a=(2a)^x  ......(1)

Log_3a2a=y    then,2a=(3a)^y ......(2)

Log_4a 3a=z  then, 3a=(4a)^z ......(3)

So, 

a=(2a)^x  [from (1)]

Or, a=(3a)^xy    [from(2)]

Or, a=(4a)^xyz     [from(3)]

Multiplying both sides by 4a,

4a.a=4a.(4a)^xyz  

Or,(2a)² =(4a)^{xyz + 1} 

Or,(3a)^2y =(4a)^xyz+1 

Or,(4a)^2yz =(4a)^xyz+1 

Or, 2yz = xyz+1 .proved.

Not even a single member ofAksionov'sfamily was concerned about his well-being when he was at his lowest.Along with the judges of the court even his wife did not trust him.Hewas imprisoned for the crime he did not commit.With time he learnt to forgive people, but he did not forget their mistreatment.

If vectors are arranged as trigonal planar and have equal magnitude, it is an ideal case of zero resultant.