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.

Compounds with hydrogen bonding tend to have higher melting and boiling points because the hydrogen bonding leads to stronger intermolecular forces. Intermolecular forces are the attractive forces between molecules, and they affect the physical properties of a substance, including melting and boiling points.

Hydrogen bonding is a particularly strong type of intermolecular force that occurs when a hydrogen atom is bonded to a highly electronegative atom such as nitrogen, oxygen, or fluorine....

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.

Yes, a vector which has zero magnitude is also a vector in case of two vectors travelling in opposite directions with equal magnitudes. At this case, the resultant vector has zero magnitude but it is still a vector. We call it a null vector.

The answer is A 

In the depletion layer, electrons combine with holes producing charge density so that region is depleted of charge carriers  but it has charge density .

Conclusion: Neutral but still having non zero charge density .